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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 161700dw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 161700.f1 | 161700dw1 | \([0, -1, 0, -3414658, -2427534563]\) | \(-359442469227794176/9021375\) | \(-110511843750000\) | \([]\) | \(2488320\) | \(2.2123\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 161700dw1 has rank \(1\).
Complex multiplication
The elliptic curves in class 161700dw do not have complex multiplication.Modular form 161700.2.a.dw
sage: E.q_eigenform(10)