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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 95550.ew
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95550.ew1 | 95550ej8 | \([1, 0, 1, -49233307401, 4204711547272198]\) | \(7179471593960193209684686321/49441793310\) | \(90887149080127968750\) | \([2]\) | \(127401984\) | \(4.3655\) | |
| 95550.ew2 | 95550ej6 | \([1, 0, 1, -3077083651, 65698338714698]\) | \(1752803993935029634719121/4599740941532100\) | \(8455545656723594264062500\) | \([2, 2]\) | \(63700992\) | \(4.0189\) | |
| 95550.ew3 | 95550ej7 | \([1, 0, 1, -3039267901, 67391803631198]\) | \(-1688971789881664420008241/89901485966373558750\) | \(-165262811288404418959042968750\) | \([2]\) | \(127401984\) | \(4.3655\) | |
| 95550.ew4 | 95550ej5 | \([1, 0, 1, -608096151, 5762203889698]\) | \(13527956825588849127121/25701087819771000\) | \(47245426264191224671875000\) | \([2]\) | \(42467328\) | \(3.8162\) | |
| 95550.ew5 | 95550ej3 | \([1, 0, 1, -194683151, 999977091698]\) | \(443915739051786565201/21894701746029840\) | \(40248277589354135096250000\) | \([2]\) | \(31850496\) | \(3.6723\) | |
| 95550.ew6 | 95550ej2 | \([1, 0, 1, -50721151, 24585639698]\) | \(7850236389974007121/4400862921000000\) | \(8089955028011390625000000\) | \([2, 2]\) | \(21233664\) | \(3.4696\) | |
| 95550.ew7 | 95550ej1 | \([1, 0, 1, -31513151, -67728008302]\) | \(1882742462388824401/11650189824000\) | \(21416143478184000000000\) | \([2]\) | \(10616832\) | \(3.1230\) | \(\Gamma_0(N)\)-optimal |
| 95550.ew8 | 95550ej4 | \([1, 0, 1, 199325849, 195117693698]\) | \(476437916651992691759/284661685546875000\) | \(-523283791295379638671875000\) | \([2]\) | \(42467328\) | \(3.8162\) |
Rank
sage: E.rank()
The elliptic curves in class 95550.ew have rank \(0\).
Complex multiplication
The elliptic curves in class 95550.ew do not have complex multiplication.Modular form 95550.2.a.ew
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
