Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 56550bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56550.cg3 | 56550bv1 | \([1, 0, 0, -44313, 3586617]\) | \(615882348586441/21715200\) | \(339300000000\) | \([2]\) | \(294912\) | \(1.3023\) | \(\Gamma_0(N)\)-optimal |
| 56550.cg2 | 56550bv2 | \([1, 0, 0, -46313, 3244617]\) | \(703093388853961/115124490000\) | \(1798820156250000\) | \([2, 2]\) | \(589824\) | \(1.6489\) | |
| 56550.cg4 | 56550bv3 | \([1, 0, 0, 84187, 18252117]\) | \(4223169036960119/11647532812500\) | \(-181992700195312500\) | \([2]\) | \(1179648\) | \(1.9955\) | |
| 56550.cg1 | 56550bv4 | \([1, 0, 0, -208813, -33642883]\) | \(64443098670429961/6032611833300\) | \(94259559895312500\) | \([2]\) | \(1179648\) | \(1.9955\) |
Rank
sage: E.rank()
The elliptic curves in class 56550bv have rank \(0\).
Complex multiplication
The elliptic curves in class 56550bv do not have complex multiplication.Modular form 56550.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
