Show commands:
SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 39600.et
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.et1 | 39600t4 | \([0, 0, 0, -158475, 24282250]\) | \(37736227588/33\) | \(384912000000\) | \([2]\) | \(196608\) | \(1.5233\) | |
| 39600.et2 | 39600t3 | \([0, 0, 0, -23475, -854750]\) | \(122657188/43923\) | \(512317872000000\) | \([2]\) | \(196608\) | \(1.5233\) | |
| 39600.et3 | 39600t2 | \([0, 0, 0, -9975, 373750]\) | \(37642192/1089\) | \(3175524000000\) | \([2, 2]\) | \(98304\) | \(1.1768\) | |
| 39600.et4 | 39600t1 | \([0, 0, 0, 150, 19375]\) | \(2048/891\) | \(-162384750000\) | \([2]\) | \(49152\) | \(0.83020\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39600.et have rank \(0\).
Complex multiplication
The elliptic curves in class 39600.et do not have complex multiplication.Modular form 39600.2.a.et
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.
