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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 75712.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75712.b1 | 75712s1 | \([0, 0, 0, -200044, -34443344]\) | \(-19983597574473/3670016\) | \(-162590281957376\) | \([]\) | \(875520\) | \(1.7297\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75712.b do not have complex multiplication.Modular form 75712.2.a.b
sage: E.q_eigenform(10)