Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 77658.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77658.j1 | 77658h1 | \([1, 1, 0, 843106, -25321833228]\) | \(5670505847/23702740992\) | \(-277042383842599002120192\) | \([]\) | \(11269440\) | \(3.1771\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 77658.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 77658.j do not have complex multiplication.Modular form 77658.2.a.j
sage: E.q_eigenform(10)