Show commands:
SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 39600.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.dv1 | 39600df3 | \([0, 0, 0, -289875, -59840750]\) | \(57736239625/255552\) | \(11923034112000000\) | \([2]\) | \(331776\) | \(1.9371\) | |
| 39600.dv2 | 39600df4 | \([0, 0, 0, -145875, -119312750]\) | \(-7357983625/127552392\) | \(-5951084401152000000\) | \([2]\) | \(663552\) | \(2.2837\) | |
| 39600.dv3 | 39600df1 | \([0, 0, 0, -19875, 1017250]\) | \(18609625/1188\) | \(55427328000000\) | \([2]\) | \(110592\) | \(1.3878\) | \(\Gamma_0(N)\)-optimal |
| 39600.dv4 | 39600df2 | \([0, 0, 0, 16125, 4293250]\) | \(9938375/176418\) | \(-8230958208000000\) | \([2]\) | \(221184\) | \(1.7344\) |
Rank
sage: E.rank()
The elliptic curves in class 39600.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 39600.dv do not have complex multiplication.Modular form 39600.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
