Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 33810.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33810.bv1 | 33810cd4 | \([1, 1, 1, -23635641, 43275013263]\) | \(12411881707829361287041/303132494474220600\) | \(35663234842397579369400\) | \([2]\) | \(5971968\) | \(3.1114\) | |
| 33810.bv2 | 33810cd2 | \([1, 1, 1, -2908641, -1887443937]\) | \(23131609187144855041/322060536000000\) | \(37890099999864000000\) | \([2]\) | \(1990656\) | \(2.5621\) | |
| 33810.bv3 | 33810cd1 | \([1, 1, 1, -23521, -79050721]\) | \(-12232183057921/22933241856000\) | \(-2698072971116544000\) | \([2]\) | \(995328\) | \(2.2156\) | \(\Gamma_0(N)\)-optimal |
| 33810.bv4 | 33810cd3 | \([1, 1, 1, 211679, 2133616799]\) | \(8915971454369279/16719623332762560\) | \(-1967046965476182421440\) | \([2]\) | \(2985984\) | \(2.7649\) |
Rank
sage: E.rank()
The elliptic curves in class 33810.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 33810.bv do not have complex multiplication.Modular form 33810.2.a.bv
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
