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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1225c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1225.j1 | 1225c1 | \([0, 0, 1, -175, 1531]\) | \(-110592/125\) | \(-669921875\) | \([]\) | \(1152\) | \(0.38796\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1225c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1225c do not have complex multiplication.Modular form 1225.2.a.c
sage: E.q_eigenform(10)