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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 109242.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 109242.p1 | 109242o3 | \([1, -1, 0, -306972, 65539858]\) | \(-545407363875/14\) | \(-82116009738\) | \([]\) | \(544320\) | \(1.6105\) | |
| 109242.p2 | 109242o1 | \([1, -1, 0, -3522, 103900]\) | \(-7414875/2744\) | \(-1788304212072\) | \([]\) | \(181440\) | \(1.0612\) | \(\Gamma_0(N)\)-optimal |
| 109242.p3 | 109242o2 | \([1, -1, 0, 26823, -1047187]\) | \(4492125/3584\) | \(-1702757577927168\) | \([]\) | \(544320\) | \(1.6105\) |
Rank
sage: E.rank()
The elliptic curves in class 109242.p have rank \(0\).
Complex multiplication
The elliptic curves in class 109242.p do not have complex multiplication.Modular form 109242.2.a.p
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
