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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5586b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5586.d1 | 5586b1 | \([1, 1, 0, -1195106203, -15902721896291]\) | \(-668286694038078762077641/413929046016\) | \(-116924710341702057984\) | \([]\) | \(1787520\) | \(3.6062\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5586b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 5586b do not have complex multiplication.Modular form 5586.2.a.b
sage: E.q_eigenform(10)