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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 12075m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12075.b1 | 12075m1 | \([0, -1, 1, -2408, -52282]\) | \(-98867482624/20696067\) | \(-323376046875\) | \([]\) | \(24000\) | \(0.93024\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12075m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12075m do not have complex multiplication.Modular form 12075.2.a.m
sage: E.q_eigenform(10)