Show commands:
SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 180336dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180336.bi3 | 180336dc1 | \([0, -1, 0, -11367, -462582]\) | \(420616192/117\) | \(45185529168\) | \([2]\) | \(327680\) | \(1.0263\) | \(\Gamma_0(N)\)-optimal |
| 180336.bi2 | 180336dc2 | \([0, -1, 0, -12812, -336000]\) | \(37642192/13689\) | \(84587310602496\) | \([2, 2]\) | \(655360\) | \(1.3729\) | |
| 180336.bi1 | 180336dc3 | \([0, -1, 0, -87952, 9822928]\) | \(3044193988/85293\) | \(2108176048862208\) | \([2]\) | \(1310720\) | \(1.7194\) | |
| 180336.bi4 | 180336dc4 | \([0, -1, 0, 39208, -2416800]\) | \(269676572/257049\) | \(-6353446885254144\) | \([2]\) | \(1310720\) | \(1.7194\) |
Rank
sage: E.rank()
The elliptic curves in class 180336dc have rank \(0\).
Complex multiplication
The elliptic curves in class 180336dc do not have complex multiplication.Modular form 180336.2.a.dc
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.
