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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 26640.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26640.w1 | 26640v1 | \([0, 0, 0, -997323, 390694522]\) | \(-991990479802737267/22190066240000\) | \(-2454043805614080000\) | \([]\) | \(414720\) | \(2.3171\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 26640.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 26640.w do not have complex multiplication.Modular form 26640.2.a.w
sage: E.q_eigenform(10)