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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 24640.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24640.r1 | 24640ba4 | \([0, 0, 0, -1338188, 595831952]\) | \(1010962818911303721/57392720\) | \(15045157191680\) | \([2]\) | \(196608\) | \(1.9951\) | |
| 24640.r2 | 24640ba3 | \([0, 0, 0, -140108, -4760432]\) | \(1160306142246441/634128110000\) | \(166232879267840000\) | \([2]\) | \(196608\) | \(1.9951\) | |
| 24640.r3 | 24640ba2 | \([0, 0, 0, -83788, 9274512]\) | \(248158561089321/1859334400\) | \(487413356953600\) | \([2, 2]\) | \(98304\) | \(1.6485\) | |
| 24640.r4 | 24640ba1 | \([0, 0, 0, -1868, 328848]\) | \(-2749884201/176619520\) | \(-46299747450880\) | \([2]\) | \(49152\) | \(1.3020\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24640.r have rank \(0\).
Complex multiplication
The elliptic curves in class 24640.r do not have complex multiplication.Modular form 24640.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
