Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 6762bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6762.y1 | 6762bd1 | \([1, 1, 1, 445703, -76671673]\) | \(83228502970940543/69854999176704\) | \(-8218370798140048896\) | \([]\) | \(190080\) | \(2.3171\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6762bd1 has rank \(0\).
Complex multiplication
The elliptic curves in class 6762bd do not have complex multiplication.Modular form 6762.2.a.bd
sage: E.q_eigenform(10)