Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 73920dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.hc3 | 73920dj1 | \([0, 1, 0, -32065, -1929697]\) | \(13908844989649/1980372240\) | \(519142700482560\) | \([2]\) | \(294912\) | \(1.5494\) | \(\Gamma_0(N)\)-optimal |
| 73920.hc2 | 73920dj2 | \([0, 1, 0, -135745, 17292575]\) | \(1055257664218129/115307784900\) | \(30227243964825600\) | \([2, 2]\) | \(589824\) | \(1.8959\) | |
| 73920.hc4 | 73920dj3 | \([0, 1, 0, 181055, 86291615]\) | \(2503876820718671/13702874328990\) | \(-3592126288098754560\) | \([2]\) | \(1179648\) | \(2.2425\) | |
| 73920.hc1 | 73920dj4 | \([0, 1, 0, -2111425, 1180177823]\) | \(3971101377248209009/56495958750\) | \(14810076610560000\) | \([4]\) | \(1179648\) | \(2.2425\) |
Rank
sage: E.rank()
The elliptic curves in class 73920dj have rank \(0\).
Complex multiplication
The elliptic curves in class 73920dj do not have complex multiplication.Modular form 73920.2.a.dj
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.
