Properties

Label 115920.a
Number of curves $4$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.a1 115920cy4 \([0, 0, 0, -69459843, -218064841342]\) \(12411881707829361287041/303132494474220600\) \(905148778380111124070400\) \([2]\) \(23887872\) \(3.3809\)  
115920.a2 115920cy2 \([0, 0, 0, -8547843, 9502649858]\) \(23131609187144855041/322060536000000\) \(961667607527424000000\) \([2]\) \(7962624\) \(2.8316\)  
115920.a3 115920cy1 \([0, 0, 0, -69123, 398200322]\) \(-12232183057921/22933241856000\) \(-68478293250146304000\) \([2]\) \(3981312\) \(2.4851\) \(\Gamma_0(N)\)-optimal
115920.a4 115920cy3 \([0, 0, 0, 622077, -10748505598]\) \(8915971454369279/16719623332762560\) \(-49924527757655679959040\) \([2]\) \(11943936\) \(3.0344\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.a have rank \(1\).

Complex multiplication

The elliptic curves in class 115920.a do not have complex multiplication.

Modular form 115920.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 6q^{11} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.