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SageMath
E = EllipticCurve("hr1")
E.isogeny_class()
Elliptic curves in class 444675hr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
444675.hr1 | 444675hr1 | \([0, -1, 1, -857908, 305091093]\) | \(313944395776/1240029\) | \(275819824849078125\) | \([]\) | \(14192640\) | \(2.2038\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 444675hr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 444675hr do not have complex multiplication.Modular form 444675.2.a.hr
sage: E.q_eigenform(10)