Properties

Label 232050fv
Number of curves $4$
Conductor $232050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fv1")
 
E.isogeny_class()
 

Elliptic curves in class 232050fv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
232050.fv4 232050fv1 \([1, 0, 0, -135688, -131008]\) \(17681870665400761/10232167895040\) \(159877623360000000\) \([2]\) \(2654208\) \(1.9906\) \(\Gamma_0(N)\)-optimal
232050.fv2 232050fv2 \([1, 0, 0, -1487688, 696148992]\) \(23304472877725373881/82743765249600\) \(1292871332025000000\) \([2, 2]\) \(5308416\) \(2.3371\)  
232050.fv1 232050fv3 \([1, 0, 0, -23782688, 44639593992]\) \(95210863233510962017081/1206641250360\) \(18853769536875000\) \([2]\) \(10616832\) \(2.6837\)  
232050.fv3 232050fv4 \([1, 0, 0, -824688, 1320031992]\) \(-3969837635175430201/45883867071315000\) \(-716935422989296875000\) \([2]\) \(10616832\) \(2.6837\)  

Rank

sage: E.rank()
 

The elliptic curves in class 232050fv have rank \(1\).

Complex multiplication

The elliptic curves in class 232050fv do not have complex multiplication.

Modular form 232050.2.a.fv

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} - 4 q^{11} + q^{12} - q^{13} - q^{14} + q^{16} - q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) Copy content 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 Cremona 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 Cremona labels.