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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 76440.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76440.w1 | 76440bx1 | \([0, -1, 0, -7660, -3028220]\) | \(-33685456/2669355\) | \(-3939404895578880\) | \([]\) | \(362880\) | \(1.6721\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 76440.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 76440.w do not have complex multiplication.Modular form 76440.2.a.w
sage: E.q_eigenform(10)