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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 111573c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111573.bf1 | 111573c1 | \([1, -1, 0, 1608, 4325]\) | \(421875/253\) | \(-275655489417\) | \([]\) | \(100352\) | \(0.88449\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 111573c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 111573c do not have complex multiplication.Modular form 111573.2.a.c
sage: E.q_eigenform(10)