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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 174570cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
174570.i1 | 174570cw1 | \([1, 1, 0, -11913, 1147113]\) | \(-2387929/5940\) | \(-465167252569140\) | \([]\) | \(715392\) | \(1.5024\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 174570cw1 has rank \(1\).
Complex multiplication
The elliptic curves in class 174570cw do not have complex multiplication.Modular form 174570.2.a.cw
sage: E.q_eigenform(10)