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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 132496j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 132496.k2 | 132496j1 | \([0, 1, 0, -971637, 368981731]\) | \(-43614208/91\) | \(-211665313528754176\) | \([]\) | \(2322432\) | \(2.2101\) | \(\Gamma_0(N)\)-optimal |
| 132496.k3 | 132496j2 | \([0, 1, 0, 1678283, 1832797539]\) | \(224755712/753571\) | \(-1752800461331613331456\) | \([]\) | \(6967296\) | \(2.7594\) | |
| 132496.k1 | 132496j3 | \([0, 1, 0, -15546197, -58153176509]\) | \(-178643795968/524596891\) | \(-1220208411095875602558976\) | \([]\) | \(20901888\) | \(3.3087\) |
Rank
sage: E.rank()
The elliptic curves in class 132496j have rank \(1\).
Complex multiplication
The elliptic curves in class 132496j do not have complex multiplication.Modular form 132496.2.a.j
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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
