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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1003.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1003.c1 | 1003b1 | \([1, 0, 1, -8, -11]\) | \(-47045881/17051\) | \(-17051\) | \([]\) | \(48\) | \(-0.47746\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1003.c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1003.c do not have complex multiplication.Modular form 1003.2.a.c
sage: E.q_eigenform(10)