Properties

Label 13872bi
Number of curves 6
Conductor 13872
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("13872.bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13872bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13872.bm5 13872bi1 [0, 1, 0, -157312, -22325068] [2] 110592 \(\Gamma_0(N)\)-optimal
13872.bm4 13872bi2 [0, 1, 0, -527232, 121351860] [2, 2] 221184  
13872.bm2 13872bi3 [0, 1, 0, -8018112, 8735863860] [2, 2] 442368  
13872.bm6 13872bi4 [0, 1, 0, 1044928, 708081972] [4] 442368  
13872.bm1 13872bi5 [0, 1, 0, -128288352, 559236806388] [2] 884736  
13872.bm3 13872bi6 [0, 1, 0, -7601952, 9683543412] [2] 884736  

Rank

sage: E.rank()
 

The elliptic curves in class 13872bi have rank \(1\).

Modular form 13872.2.a.bm

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} + q^{9} - 4q^{11} - 2q^{13} + 2q^{15} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.