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SageMath
E = EllipticCurve("im1")
E.isogeny_class()
Elliptic curves in class 177450im
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177450.x1 | 177450im1 | \([1, 1, 0, -8460650, 10401995700]\) | \(-22202140659489025/2656521215712\) | \(-8014075320431014380000\) | \([]\) | \(13547520\) | \(2.9384\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 177450im1 has rank \(0\).
Complex multiplication
The elliptic curves in class 177450im do not have complex multiplication.Modular form 177450.2.a.im
sage: E.q_eigenform(10)