Show commands:
SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 115920dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.dj3 | 115920dx1 | \([0, 0, 0, -21747, 1198514]\) | \(380920459249/12622400\) | \(37690284441600\) | \([2]\) | \(331776\) | \(1.3781\) | \(\Gamma_0(N)\)-optimal |
| 115920.dj4 | 115920dx2 | \([0, 0, 0, 7053, 4141874]\) | \(12994449551/2489452840\) | \(-7433466348994560\) | \([2]\) | \(663552\) | \(1.7246\) | |
| 115920.dj1 | 115920dx3 | \([0, 0, 0, -243507, -45850894]\) | \(534774372149809/5323062500\) | \(15894579456000000\) | \([2]\) | \(995328\) | \(1.9274\) | |
| 115920.dj2 | 115920dx4 | \([0, 0, 0, -63507, -112126894]\) | \(-9486391169809/1813439640250\) | \(-5414901750752256000\) | \([2]\) | \(1990656\) | \(2.2739\) |
Rank
sage: E.rank()
The elliptic curves in class 115920dx have rank \(0\).
Complex multiplication
The elliptic curves in class 115920dx do not have complex multiplication.Modular form 115920.2.a.dx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
