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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 450840cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 450840.cu1 | 450840cu1 | \([0, 1, 0, -3761720, 16612749600]\) | \(-824122740964/16216331625\) | \(-115836104702788988544000\) | \([]\) | \(42301440\) | \(3.1065\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 450840cu1 has rank \(0\).
Complex multiplication
The elliptic curves in class 450840cu do not have complex multiplication.Modular form 450840.2.a.cu
sage: E.q_eigenform(10)