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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 100005.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100005.c1 | 100005d1 | \([1, 0, 1, -1133, -77407]\) | \(-160643187047881/2489186953125\) | \(-2489186953125\) | \([]\) | \(180096\) | \(1.0599\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100005.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100005.c do not have complex multiplication.Modular form 100005.2.a.c
sage: E.q_eigenform(10)