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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4033.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4033.b1 | 4033b1 | \([1, -1, 0, 10717, 157106]\) | \(136119582814177143/89802435289753\) | \(-89802435289753\) | \([]\) | \(7560\) | \(1.3662\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4033.b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4033.b do not have complex multiplication.Modular form 4033.2.a.b
sage: E.q_eigenform(10)