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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 17640.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17640.c1 | 17640m1 | \([0, 0, 0, -588, 10388]\) | \(-50176/75\) | \(-33606316800\) | \([]\) | \(15360\) | \(0.71157\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 17640.c1 has rank \(2\).
Complex multiplication
The elliptic curves in class 17640.c do not have complex multiplication.Modular form 17640.2.a.c
sage: E.q_eigenform(10)