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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1613.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1613.a1 | 1613a1 | \([0, 1, 1, -3, 0]\) | \(4096000/1613\) | \(1613\) | \([]\) | \(80\) | \(-0.68600\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1613.a1 has rank \(2\).
Complex multiplication
The elliptic curves in class 1613.a do not have complex multiplication.Modular form 1613.2.a.a
sage: E.q_eigenform(10)