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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 8925.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8925.y1 | 8925q3 | \([1, 0, 1, -25376, 1198523]\) | \(115650783909361/27072079335\) | \(423001239609375\) | \([2]\) | \(36864\) | \(1.5184\) | |
| 8925.y2 | 8925q2 | \([1, 0, 1, -8501, -286477]\) | \(4347507044161/258084225\) | \(4032566015625\) | \([2, 2]\) | \(18432\) | \(1.1718\) | |
| 8925.y3 | 8925q1 | \([1, 0, 1, -8376, -295727]\) | \(4158523459441/16065\) | \(251015625\) | \([2]\) | \(9216\) | \(0.82522\) | \(\Gamma_0(N)\)-optimal |
| 8925.y4 | 8925q4 | \([1, 0, 1, 6374, -1178977]\) | \(1833318007919/39525924375\) | \(-617592568359375\) | \([2]\) | \(36864\) | \(1.5184\) |
Rank
sage: E.rank()
The elliptic curves in class 8925.y have rank \(0\).
Complex multiplication
The elliptic curves in class 8925.y do not have complex multiplication.Modular form 8925.2.a.y
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
