Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 17600bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17600.cp4 | 17600bv1 | \([0, -1, 0, -4533, -113563]\) | \(643956736/15125\) | \(242000000000\) | \([2]\) | \(27648\) | \(0.96986\) | \(\Gamma_0(N)\)-optimal |
| 17600.cp3 | 17600bv2 | \([0, -1, 0, -10033, 221937]\) | \(436334416/171875\) | \(44000000000000\) | \([2]\) | \(55296\) | \(1.3164\) | |
| 17600.cp2 | 17600bv3 | \([0, -1, 0, -44533, 3586437]\) | \(610462990336/8857805\) | \(141724880000000\) | \([2]\) | \(82944\) | \(1.5192\) | |
| 17600.cp1 | 17600bv4 | \([0, -1, 0, -710033, 230521937]\) | \(154639330142416/33275\) | \(8518400000000\) | \([2]\) | \(165888\) | \(1.8657\) |
Rank
sage: E.rank()
The elliptic curves in class 17600bv have rank \(0\).
Complex multiplication
The elliptic curves in class 17600bv do not have complex multiplication.Modular form 17600.2.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 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.
