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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 129.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129.a1 | 129a1 | \([0, -1, 1, -19, 39]\) | \(-799178752/3483\) | \(-3483\) | \([]\) | \(8\) | \(-0.46711\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 129.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 129.a do not have complex multiplication.Modular form 129.2.a.a
sage: E.q_eigenform(10)