Discussion for elliptic curves
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Home page for Elliptic curves in general
- Torsion structures over different fields.
- Distribution of ranks.
- first conductor for rank 0, 1, 2, 3, ...
- in families of twists
- by conductor
- number of isogeny classes by conductor
- number of isomorphism classes by conductor
Home page for a given conductor N
- Isogeny classes
- Isomorphism classes
- number of torsion structures?
friend link to space of modular newforms of weight 2 and level N
Home page for an isogeny class of elliptic curves
- minimal weierstrass equation
- cremona label, if it exists
conductor N, with factorization
- analytic order of sha
- regulator
\Omega(E)
- rank
- tamagawa numbers
- leading term of the Taylor series of L-fn
- same, for p-adic L-fn
- p-adic regulator
- Mordell-Weil generators
- isogeny class data (e.g. isogeny graph picture)
- Hecke eigenvalues
- Manin constant
- torsion structures across isogeny class
- actual order of sha, with proofs, including:
- heegner indexes used
p-adic regulator
- descent data if relevant
- local signs of the functional equation
- explicit elements of Sha
- Tom Fisher's data of 5- and 7-torsion in Sha
- Cremona-Mazur visibility information
- bounds coming from Grigorov's thesis?
- friends:
- Associated L-function
- Associated modular form
- Sym^2
- twists
- curves at other levels whose M-W group visualizes Sha
Homepage for a specific elliptic curve
- Information to add
- primes of bad reduction
- discriminant
- Kodaira type of bad fibers
- extra L-function information (sign of functional equation)
- structure of torsion
- GP, Sage, Magma code/exfiltration
- (known) integral points
- why not hand off modular form expansion to Modular Form?