Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("dp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.dp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dp1 115920bj4 \([0, 0, 0, -875666307, -8747613671326]\) \(49737293673675178002921218/6641736806881023047235\) \(9916059918778912361337477120\) \([2]\) \(70778880\) \(4.0996\)  
115920.dp2 115920bj2 \([0, 0, 0, -845413707, -9461145444406]\) \(89516703758060574923008036/1985322833430374025\) \(1482035553864440488166400\) \([2, 2]\) \(35389440\) \(3.7531\)  
115920.dp3 115920bj1 \([0, 0, 0, -845409207, -9461251202506]\) \(358061097267989271289240144/176126855625\) \(32869498304160000\) \([2]\) \(17694720\) \(3.4065\) \(\Gamma_0(N)\)-optimal
115920.dp4 115920bj3 \([0, 0, 0, -815233107, -10167908699086]\) \(-40133926989810174413190818/6689384645060302103835\) \(-9987197759997870558608824320\) \([2]\) \(70778880\) \(4.0996\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.dp

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + 4 q^{11} - 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.