Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 5712z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5712.w1 | 5712z1 | \([0, 1, 0, 57035, -4723549]\) | \(5009339741732864/5271114033171\) | \(-21590483079868416\) | \([]\) | \(39168\) | \(1.8210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5712z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5712z do not have complex multiplication.Modular form 5712.2.a.z
sage: E.q_eigenform(10)