Show commands:
SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 37440ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.cu4 | 37440ep1 | \([0, 0, 0, 537, 4808]\) | \(367061696/426465\) | \(-19897151040\) | \([2]\) | \(24576\) | \(0.66248\) | \(\Gamma_0(N)\)-optimal |
| 37440.cu3 | 37440ep2 | \([0, 0, 0, -3108, 45632]\) | \(1111934656/342225\) | \(1021878374400\) | \([2, 2]\) | \(49152\) | \(1.0091\) | |
| 37440.cu2 | 37440ep3 | \([0, 0, 0, -19308, -997648]\) | \(33324076232/1285245\) | \(30701768048640\) | \([2]\) | \(98304\) | \(1.3556\) | |
| 37440.cu1 | 37440ep4 | \([0, 0, 0, -45228, 3701648]\) | \(428320044872/73125\) | \(1746800640000\) | \([2]\) | \(98304\) | \(1.3556\) |
Rank
sage: E.rank()
The elliptic curves in class 37440ep have rank \(0\).
Complex multiplication
The elliptic curves in class 37440ep do not have complex multiplication.Modular form 37440.2.a.ep
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.
