Properties

Label 40432r
Number of curves 6
Conductor 40432
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("40432.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40432r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40432.b5 40432r1 [0, 1, 0, -3008, 127540] [2] 57024 \(\Gamma_0(N)\)-optimal
40432.b4 40432r2 [0, 1, 0, -60768, 5741812] [2] 114048  
40432.b6 40432r3 [0, 1, 0, 25872, -2679596] [2] 171072  
40432.b3 40432r4 [0, 1, 0, -205168, -29387820] [2] 342144  
40432.b2 40432r5 [0, 1, 0, -984928, -377645964] [2] 513216  
40432.b1 40432r6 [0, 1, 0, -15771488, -24113032076] [2] 1026432  

Rank

sage: E.rank()
 

The elliptic curves in class 40432r have rank \(1\).

Modular form 40432.2.a.b

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - q^{7} + q^{9} + 4q^{13} + 6q^{17} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.