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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 24684.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24684.f1 | 24684f1 | \([0, -1, 0, -275557, 2272404433]\) | \(-5102271397888/4915446963867\) | \(-2229251619521327715072\) | \([]\) | \(1935360\) | \(2.7754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 24684.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 24684.f do not have complex multiplication.Modular form 24684.2.a.f
sage: E.q_eigenform(10)