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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 722.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
722.f1 | 722d1 | \([1, -1, 1, -429, 77485]\) | \(-27/8\) | \(-2581501582232\) | \([]\) | \(2280\) | \(1.0608\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 722.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 722.f do not have complex multiplication.Modular form 722.2.a.f
sage: E.q_eigenform(10)