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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 5850.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5850.a1 | 5850s1 | \([1, -1, 0, 18, -54]\) | \(34295/78\) | \(-1421550\) | \([]\) | \(1344\) | \(-0.13531\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5850.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5850.a do not have complex multiplication.Modular form 5850.2.a.a
sage: E.q_eigenform(10)