Show commands:
SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 115920dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.j1 | 115920dc1 | \([0, 0, 0, -33123, -1993822]\) | \(1345938541921/203765625\) | \(608440896000000\) | \([2]\) | \(393216\) | \(1.5608\) | \(\Gamma_0(N)\)-optimal |
| 115920.j2 | 115920dc2 | \([0, 0, 0, 56877, -10939822]\) | \(6814692748079/21258460125\) | \(-63477421797888000\) | \([2]\) | \(786432\) | \(1.9074\) |
Rank
sage: E.rank()
The elliptic curves in class 115920dc have rank \(0\).
Complex multiplication
The elliptic curves in class 115920dc do not have complex multiplication.Modular form 115920.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
