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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 115920.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.cq1 | 115920eo4 | \([0, 0, 0, -618267, 187116554]\) | \(8753151307882969/65205\) | \(194701086720\) | \([2]\) | \(720896\) | \(1.7608\) | |
| 115920.cq2 | 115920eo2 | \([0, 0, 0, -38667, 2919674]\) | \(2141202151369/5832225\) | \(17414930534400\) | \([2, 2]\) | \(360448\) | \(1.4142\) | |
| 115920.cq3 | 115920eo3 | \([0, 0, 0, -23547, 5226986]\) | \(-483551781049/3672913125\) | \(-10967259824640000\) | \([4]\) | \(720896\) | \(1.7608\) | |
| 115920.cq4 | 115920eo1 | \([0, 0, 0, -3387, 5546]\) | \(1439069689/828345\) | \(2473424916480\) | \([2]\) | \(180224\) | \(1.0676\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.cq have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.cq do not have complex multiplication.Modular form 115920.2.a.cq
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.
