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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6909c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6909.a1 | 6909c1 | \([0, -1, 1, -604, -1968]\) | \(207474688/102789\) | \(12093023061\) | \([]\) | \(9240\) | \(0.62769\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6909c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 6909c do not have complex multiplication.Modular form 6909.2.a.c
sage: E.q_eigenform(10)