Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 3330.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3330.s1 | 3330y3 | \([1, -1, 1, -3224862977, 70488777789969]\) | \(5087799435928552778197163696329/125914832087040\) | \(91791912591452160\) | \([2]\) | \(1576960\) | \(3.7005\) | |
| 3330.s2 | 3330y2 | \([1, -1, 1, -201554177, 1101422182929]\) | \(1242142983306846366056931529/6179359141291622400\) | \(4504752814001592729600\) | \([2, 2]\) | \(788480\) | \(3.3539\) | |
| 3330.s3 | 3330y4 | \([1, -1, 1, -198144257, 1140484862481]\) | \(-1180159344892952613848670409/87759036144023189760000\) | \(-63976337348992905335040000\) | \([2]\) | \(1576960\) | \(3.7005\) | |
| 3330.s4 | 3330y1 | \([1, -1, 1, -12810497, 16599007761]\) | \(318929057401476905525449/21353131537921474560\) | \(15566432891144754954240\) | \([2]\) | \(394240\) | \(3.0073\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3330.s have rank \(0\).
Complex multiplication
The elliptic curves in class 3330.s do not have complex multiplication.Modular form 3330.2.a.s
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
