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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 279174r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
279174.r1 | 279174r1 | \([1, 1, 0, 167759, 19298773]\) | \(4402880119/3894912\) | \(-461889343222683264\) | \([]\) | \(4569600\) | \(2.0770\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 279174r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 279174r do not have complex multiplication.Modular form 279174.2.a.r
sage: E.q_eigenform(10)