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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 476850w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 476850.w1 | 476850w1 | \([1, 1, 0, -686989275, 6932659780125]\) | \(-27476276164729743854449/10604287663073280\) | \(-13838761092305365920000000\) | \([]\) | \(250069248\) | \(3.7896\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 476850w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 476850w do not have complex multiplication.Modular form 476850.2.a.w
sage: E.q_eigenform(10)