Show commands:
SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 487872gm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.gm1 | 487872gm1 | \([0, 0, 0, -143748, -15021666]\) | \(1216512/343\) | \(92620445962879296\) | \([]\) | \(3041280\) | \(1.9625\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 487872gm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 487872gm do not have complex multiplication.Modular form 487872.2.a.gm
sage: E.q_eigenform(10)