Show commands:
SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 34650.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34650.dv1 | 34650di4 | \([1, -1, 1, -9055580, -10486456203]\) | \(7209828390823479793/49509306\) | \(563941938656250\) | \([2]\) | \(786432\) | \(2.4303\) | |
| 34650.dv2 | 34650di3 | \([1, -1, 1, -789080, -22750203]\) | \(4770223741048753/2740574865798\) | \(31216860580730343750\) | \([2]\) | \(786432\) | \(2.4303\) | |
| 34650.dv3 | 34650di2 | \([1, -1, 1, -566330, -163528203]\) | \(1763535241378513/4612311396\) | \(52537109495062500\) | \([2, 2]\) | \(393216\) | \(2.0837\) | |
| 34650.dv4 | 34650di1 | \([1, -1, 1, -21830, -4534203]\) | \(-100999381393/723148272\) | \(-8237110785750000\) | \([2]\) | \(196608\) | \(1.7371\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34650.dv have rank \(0\).
Complex multiplication
The elliptic curves in class 34650.dv do not have complex multiplication.Modular form 34650.2.a.dv
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.
