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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 78400fr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.kt1 | 78400fr1 | \([0, 0, 0, -196000, -34300000]\) | \(-221184/7\) | \(-26353376000000000\) | \([]\) | \(1105920\) | \(1.9271\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400fr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 78400fr do not have complex multiplication.Modular form 78400.2.a.fr
sage: E.q_eigenform(10)