Properties

Label 152880.i
Number of curves $6$
Conductor $152880$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("152880.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 152880.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
152880.i1 152880ee6 [0, -1, 0, -7067776, -7229874560] [2] 4718592  
152880.i2 152880ee3 [0, -1, 0, -662496, 207607296] [2] 2359296  
152880.i3 152880ee4 [0, -1, 0, -442976, -112189440] [2, 2] 2359296  
152880.i4 152880ee5 [0, -1, 0, -90176, -286331520] [2] 4718592  
152880.i5 152880ee2 [0, -1, 0, -50976, 1647360] [2, 2] 1179648  
152880.i6 152880ee1 [0, -1, 0, 11744, 192256] [2] 589824 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 152880.i have rank \(1\).

Modular form 152880.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} - 4q^{11} - q^{13} + q^{15} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.