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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 11642.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11642.a1 | 11642a1 | \([1, -1, 0, -16, 28]\) | \(469097433/23284\) | \(23284\) | \([]\) | \(4624\) | \(-0.40304\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 11642.a1 has rank \(3\).
Complex multiplication
The elliptic curves in class 11642.a do not have complex multiplication.Modular form 11642.2.a.a
sage: E.q_eigenform(10)