Show commands:
SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 57330bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57330.l1 | 57330bm1 | \([1, -1, 0, -374700510, 2792197807636]\) | \(-28253264609835195889/4297784624640\) | \(-885018963073301985277440\) | \([]\) | \(16450560\) | \(3.6075\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 57330bm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 57330bm do not have complex multiplication.Modular form 57330.2.a.bm
sage: E.q_eigenform(10)