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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 456.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
456.a1 | 456d1 | \([0, -1, 0, 55, 93]\) | \(70575104/61731\) | \(-15803136\) | \([]\) | \(96\) | \(0.068805\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 456.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 456.a do not have complex multiplication.Modular form 456.2.a.a
sage: E.q_eigenform(10)