Properties

Label 25392.be
Number of curves $6$
Conductor $25392$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25392.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25392.be1 25392g6 \([0, 1, 0, -203312, -35352972]\) \(3065617154/9\) \(2728597506048\) \([2]\) \(90112\) \(1.6155\)  
25392.be2 25392g4 \([0, 1, 0, -34032, 2404932]\) \(28756228/3\) \(454766251008\) \([2]\) \(45056\) \(1.2690\)  
25392.be3 25392g3 \([0, 1, 0, -12872, -540540]\) \(1556068/81\) \(12278688777216\) \([2, 2]\) \(45056\) \(1.2690\)  
25392.be4 25392g2 \([0, 1, 0, -2292, 30780]\) \(35152/9\) \(341074688256\) \([2, 2]\) \(22528\) \(0.92239\)  
25392.be5 25392g1 \([0, 1, 0, 353, 3272]\) \(2048/3\) \(-7105722672\) \([2]\) \(11264\) \(0.57582\) \(\Gamma_0(N)\)-optimal
25392.be6 25392g5 \([0, 1, 0, 8288, -2123308]\) \(207646/6561\) \(-1989147581908992\) \([2]\) \(90112\) \(1.6155\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25392.be have rank \(1\).

Complex multiplication

The elliptic curves in class 25392.be do not have complex multiplication.

Modular form 25392.2.a.be

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2q^{5} + q^{9} + 4q^{11} - 2q^{13} + 2q^{15} - 2q^{17} - 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.