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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 62790.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62790.bu1 | 62790bt8 | \([1, 0, 0, -43057798550, 3438429180592800]\) | \(8828342566147309471108534663879471201/1536341563898865415843582949700\) | \(1536341563898865415843582949700\) | \([2]\) | \(228261888\) | \(4.7978\) | |
| 62790.bu2 | 62790bt5 | \([1, 0, 0, -43056000050, 3438730826002500]\) | \(8827236347661221188886967161105287201/46539238473000000\) | \(46539238473000000\) | \([6]\) | \(76087296\) | \(4.2485\) | |
| 62790.bu3 | 62790bt7 | \([1, 0, 0, -18469941230, -933806241069048]\) | \(696819431300451649932999125896765921/26551778102890598266349123437500\) | \(26551778102890598266349123437500\) | \([2]\) | \(228261888\) | \(4.7978\) | |
| 62790.bu4 | 62790bt6 | \([1, 0, 0, -2961450050, 42276481912500]\) | \(2872347286043717137884962530087201/890114999660918118510786090000\) | \(890114999660918118510786090000\) | \([2, 2]\) | \(114130944\) | \(4.4512\) | |
| 62790.bu5 | 62790bt4 | \([1, 0, 0, -2696503730, 53499182368452]\) | \(2168337038351679228688694521765921/18360082088470458984375000000\) | \(18360082088470458984375000000\) | \([6]\) | \(76087296\) | \(4.2485\) | |
| 62790.bu6 | 62790bt2 | \([1, 0, 0, -2691000050, 53729999002500]\) | \(2155087111607167363355460545287201/156481162929000000000000\) | \(156481162929000000000000\) | \([2, 6]\) | \(38043648\) | \(3.9019\) | |
| 62790.bu7 | 62790bt1 | \([1, 0, 0, -167843570, 843125287812]\) | \(-522923112164227281987660878881/4484275679769919488000000\) | \(-4484275679769919488000000\) | \([12]\) | \(19021824\) | \(3.5554\) | \(\Gamma_0(N)\)-optimal |
| 62790.bu8 | 62790bt3 | \([1, 0, 0, 513852430, 4463105748612]\) | \(15005102139088880168192111025119/17288486242801155608083603200\) | \(-17288486242801155608083603200\) | \([4]\) | \(57065472\) | \(4.1047\) |
Rank
sage: E.rank()
The elliptic curves in class 62790.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 62790.bu do not have complex multiplication.Modular form 62790.2.a.bu
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 2 & 12 & 6 & 12 & 4 \\ 3 & 1 & 12 & 6 & 4 & 2 & 4 & 12 \\ 4 & 12 & 1 & 2 & 3 & 6 & 12 & 4 \\ 2 & 6 & 2 & 1 & 6 & 3 & 6 & 2 \\ 12 & 4 & 3 & 6 & 1 & 2 & 4 & 12 \\ 6 & 2 & 6 & 3 & 2 & 1 & 2 & 6 \\ 12 & 4 & 12 & 6 & 4 & 2 & 1 & 3 \\ 4 & 12 & 4 & 2 & 12 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
