Show commands:
SageMath
E = EllipticCurve("gf1")
E.isogeny_class()
Elliptic curves in class 62400gf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.fc1 | 62400gf1 | \([0, 1, 0, -587283, -175561437]\) | \(-22400965661211136/321826171875\) | \(-321826171875000000\) | \([]\) | \(709632\) | \(2.1643\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 62400gf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 62400gf do not have complex multiplication.Modular form 62400.2.a.gf
sage: E.q_eigenform(10)