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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 666.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
666.b1 | 666b1 | \([1, -1, 0, 153, -4685]\) | \(541343375/13108878\) | \(-9556372062\) | \([]\) | \(352\) | \(0.59524\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 666.b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 666.b do not have complex multiplication.Modular form 666.2.a.b
sage: E.q_eigenform(10)