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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 644.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
644.a1 | 644b1 | \([0, -1, 0, 2, -7]\) | \(32000/1127\) | \(-18032\) | \([]\) | \(24\) | \(-0.50341\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 644.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 644.a do not have complex multiplication.Modular form 644.2.a.a
sage: E.q_eigenform(10)