Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 138720.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 138720.l1 | 138720bj4 | \([0, -1, 0, -1040785, -408338975]\) | \(1261112198464/675\) | \(66735550771200\) | \([2]\) | \(1966080\) | \(1.9822\) | |
| 138720.l2 | 138720bj2 | \([0, -1, 0, -143440, 11688712]\) | \(26410345352/10546875\) | \(130342872600000000\) | \([2]\) | \(1966080\) | \(1.9822\) | |
| 138720.l3 | 138720bj1 | \([0, -1, 0, -65410, -6289400]\) | \(20034997696/455625\) | \(703851512040000\) | \([2, 2]\) | \(983040\) | \(1.6357\) | \(\Gamma_0(N)\)-optimal |
| 138720.l4 | 138720bj3 | \([0, -1, 0, 6840, -19496700]\) | \(2863288/13286025\) | \(-164194480728691200\) | \([2]\) | \(1966080\) | \(1.9822\) |
Rank
sage: E.rank()
The elliptic curves in class 138720.l have rank \(0\).
Complex multiplication
The elliptic curves in class 138720.l do not have complex multiplication.Modular form 138720.2.a.l
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.
