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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 84966t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84966.z4 | 84966t1 | \([1, 1, 0, -2612999, -1532580363]\) | \(141420761/9216\) | \(128579282675671016448\) | \([2]\) | \(3916800\) | \(2.6085\) | \(\Gamma_0(N)\)-optimal |
| 84966.z3 | 84966t2 | \([1, 1, 0, -41130919, -101548211435]\) | \(551569744601/2592\) | \(36162923252532473376\) | \([2]\) | \(7833600\) | \(2.9551\) | |
| 84966.z2 | 84966t3 | \([1, 1, 0, -296312139, 1963109558313]\) | \(206226044828441/236196\) | \(3295346381387021636388\) | \([2]\) | \(19584000\) | \(3.4132\) | |
| 84966.z1 | 84966t4 | \([1, 1, 0, -298719509, 1929585968115]\) | \(211293405175481/6973568802\) | \(97293454237261120303537506\) | \([2]\) | \(39168000\) | \(3.7598\) |
Rank
sage: E.rank()
The elliptic curves in class 84966t have rank \(0\).
Complex multiplication
The elliptic curves in class 84966t do not have complex multiplication.Modular form 84966.2.a.t
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
