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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 29040c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29040.q1 | 29040c1 | \([0, -1, 0, -28349856, -57948973344]\) | \(5739907130357378/16142520375\) | \(7086679253206426368000\) | \([]\) | \(2154240\) | \(3.0648\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 29040c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 29040c do not have complex multiplication.Modular form 29040.2.a.c
sage: E.q_eigenform(10)