Properties

Label 83259l
Number of curves 4
Conductor 83259
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("83259.m1")
sage: E.isogeny_class()

Elliptic curves in class 83259l

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
83259.m3 83259l1 [1, -1, 0, -49356, 4197339] 2 290304 \(\Gamma_0(N)\)-optimal
83259.m2 83259l2 [1, -1, 0, -87201, -3091608] 4 580608  
83259.m4 83259l3 [1, -1, 0, 329094, -24322653] 2 1161216  
83259.m1 83259l4 [1, -1, 0, -1109016, -448807311] 2 1161216  

Rank

sage: E.rank()

The elliptic curves in class 83259l have rank \(1\).

Modular form 83259.2.a.m

sage: E.q_eigenform(10)
\( q + q^{2} - q^{4} + 2q^{5} + 4q^{7} - 3q^{8} + 2q^{10} + q^{11} - 2q^{13} + 4q^{14} - q^{16} - 2q^{17} + O(q^{20}) \)

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.