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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 58800.cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.cm1 | 58800bs1 | \([0, -1, 0, -90237583, -337026913838]\) | \(-46028377077760/1162261467\) | \(-2051938108087064268750000\) | \([]\) | \(7660800\) | \(3.4492\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 58800.cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 58800.cm do not have complex multiplication.Modular form 58800.2.a.cm
sage: E.q_eigenform(10)