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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4725.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4725.c1 | 4725g1 | \([0, 0, 1, -675, -844]\) | \(12288/7\) | \(19375453125\) | \([]\) | \(5040\) | \(0.66376\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4725.c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4725.c do not have complex multiplication.Modular form 4725.2.a.c
sage: E.q_eigenform(10)