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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 643.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
643.a1 | 643a1 | \([1, 0, 0, -4, 3]\) | \(-7189057/643\) | \(-643\) | \([]\) | \(32\) | \(-0.71774\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 643.a1 has rank \(2\).
Complex multiplication
The elliptic curves in class 643.a do not have complex multiplication.Modular form 643.2.a.a
sage: E.q_eigenform(10)