Show commands:
SageMath
E = EllipticCurve("es1")
E.isogeny_class()
Elliptic curves in class 78400.es
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.es1 | 78400hc1 | \([0, 0, 0, -140, -560]\) | \(7560\) | \(40140800\) | \([]\) | \(20736\) | \(0.18691\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400.es1 has rank \(1\).
Complex multiplication
The elliptic curves in class 78400.es do not have complex multiplication.Modular form 78400.2.a.es
sage: E.q_eigenform(10)