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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 17424.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17424.r1 | 17424bv3 | \([0, 0, 0, -136261488, 612220410736]\) | \(-52893159101157376/11\) | \(-58188380811264\) | \([]\) | \(720000\) | \(2.9381\) | |
| 17424.r2 | 17424bv2 | \([0, 0, 0, -180048, 53261296]\) | \(-122023936/161051\) | \(-851936083457716224\) | \([]\) | \(144000\) | \(2.1334\) | |
| 17424.r3 | 17424bv1 | \([0, 0, 0, -5808, -404624]\) | \(-4096/11\) | \(-58188380811264\) | \([]\) | \(28800\) | \(1.3287\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17424.r have rank \(0\).
Complex multiplication
The elliptic curves in class 17424.r do not have complex multiplication.Modular form 17424.2.a.r
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
