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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 161700.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 161700.x1 | 161700ee1 | \([0, -1, 0, -7033133, -7178671863]\) | \(-81756451446784/24958395\) | \(-11745320853420000000\) | \([]\) | \(4976640\) | \(2.6363\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 161700.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 161700.x do not have complex multiplication.Modular form 161700.2.a.x
sage: E.q_eigenform(10)