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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 5692.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5692.a1 | 5692a1 | \([0, 1, 0, -18, 25]\) | \(-42592000/1423\) | \(-22768\) | \([]\) | \(516\) | \(-0.38957\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5692.a1 has rank \(2\).
Complex multiplication
The elliptic curves in class 5692.a do not have complex multiplication.Modular form 5692.2.a.a
sage: E.q_eigenform(10)