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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 97175w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97175.z1 | 97175w1 | \([0, 1, 1, -3098, 65589]\) | \(-5451776/23\) | \(-13877075875\) | \([]\) | \(129024\) | \(0.80077\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 97175w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 97175w do not have complex multiplication.Modular form 97175.2.a.w
sage: E.q_eigenform(10)