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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 37.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37.a1 | 37a1 | \([0, 0, 1, -1, 0]\) | \(110592/37\) | \(37\) | \([]\) | \(2\) | \(-0.99654\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 37.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 37.a do not have complex multiplication.Modular form 37.2.a.a
sage: E.q_eigenform(10)