Show commands:
SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 75456cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75456.bi1 | 75456cl1 | \([0, 0, 0, -1969068, -1063503664]\) | \(4418129129836969/2291976\) | \(438003434520576\) | \([]\) | \(774144\) | \(2.1409\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75456cl1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75456cl do not have complex multiplication.Modular form 75456.2.a.cl
sage: E.q_eigenform(10)