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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 69300.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69300.w1 | 69300r1 | \([0, 0, 0, -41444757000, 3247525504462500]\) | \(-799965408846201776676864/128959272851717\) | \(-1269152683770172855500000000\) | \([]\) | \(95247360\) | \(4.6029\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 69300.w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 69300.w do not have complex multiplication.Modular form 69300.2.a.w
sage: E.q_eigenform(10)