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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4004.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4004.b1 | 4004a1 | \([0, -1, 0, -2717, -54791]\) | \(-8667872124928/218709491\) | \(-55989629696\) | \([]\) | \(3168\) | \(0.84650\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4004.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4004.b do not have complex multiplication.Modular form 4004.2.a.b
sage: E.q_eigenform(10)