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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 303450cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.cm1 | 303450cm1 | \([1, 0, 1, -3126, -40952]\) | \(18694465225/6858432\) | \(1238804280000\) | \([]\) | \(798336\) | \(1.0207\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 303450cm1 has rank \(2\).
Complex multiplication
The elliptic curves in class 303450cm do not have complex multiplication.Modular form 303450.2.a.cm
sage: E.q_eigenform(10)