↑

Properties

Label 13754d
Number of curves $3$
Conductor $13754$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 13754d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13754.e3 13754d1 \([1, 0, 1, 253, -2528]\) \(12167/26\) \(-3848933114\) \([]\) \(8448\) \(0.52352\) \(\Gamma_0(N)\)-optimal
13754.e2 13754d2 \([1, 0, 1, -2392, 89518]\) \(-10218313/17576\) \(-2601878785064\) \([]\) \(25344\) \(1.0728\)  
13754.e1 13754d3 \([1, 0, 1, -243087, 46110402]\) \(-10730978619193/6656\) \(-985326877184\) \([]\) \(76032\) \(1.6221\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13754d have rank \(1\).

Complex multiplication

The elliptic curves in class 13754d do not have complex multiplication.

Modular form 13754.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} + q^{7} - q^{8} - 2 q^{9} - 3 q^{10} - 6 q^{11} + q^{12} + q^{13} - q^{14} + 3 q^{15} + q^{16} + 3 q^{17} + 2 q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.