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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 135.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
135.b1 | 135b1 | \([0, 0, 1, -27, -115]\) | \(-12288/25\) | \(-4428675\) | \([]\) | \(36\) | \(-0.035421\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 135.b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 135.b do not have complex multiplication.Modular form 135.2.a.b
sage: E.q_eigenform(10)