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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 49725a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49725.l1 | 49725a1 | \([0, 0, 1, -180450, 47736156]\) | \(-1540318675894272/1442042265625\) | \(-608361580810546875\) | \([]\) | \(510720\) | \(2.1089\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 49725a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 49725a do not have complex multiplication.Modular form 49725.2.a.a
sage: E.q_eigenform(10)