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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 4275m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4275.c1 | 4275m1 | \([1, -1, 1, -140, 672]\) | \(-16539745/57\) | \(-1038825\) | \([]\) | \(768\) | \(0.017835\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4275m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4275m do not have complex multiplication.Modular form 4275.2.a.m
sage: E.q_eigenform(10)