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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 66240bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66240.bx3 | 66240bt1 | \([0, 0, 0, -4188, 104272]\) | \(680136784/345\) | \(4120657920\) | \([2]\) | \(49152\) | \(0.79696\) | \(\Gamma_0(N)\)-optimal |
| 66240.bx2 | 66240bt2 | \([0, 0, 0, -4908, 65968]\) | \(273671716/119025\) | \(5686507929600\) | \([2, 2]\) | \(98304\) | \(1.1435\) | |
| 66240.bx4 | 66240bt3 | \([0, 0, 0, 16692, 489328]\) | \(5382838942/4197615\) | \(-401088359301120\) | \([2]\) | \(196608\) | \(1.4901\) | |
| 66240.bx1 | 66240bt4 | \([0, 0, 0, -38028, -2808848]\) | \(63649751618/1164375\) | \(111257763840000\) | \([2]\) | \(196608\) | \(1.4901\) |
Rank
sage: E.rank()
The elliptic curves in class 66240bt have rank \(1\).
Complex multiplication
The elliptic curves in class 66240bt do not have complex multiplication.Modular form 66240.2.a.bt
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
