Properties

Label 3120.w
Number of curves $6$
Conductor $3120$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("3120.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3120.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3120.w1 3120z5 [0, 1, 0, -144240, 21037140] [4] 12288  
3120.w2 3120z3 [0, 1, 0, -13520, -609132] [2] 6144  
3120.w3 3120z4 [0, 1, 0, -9040, 324500] [2, 4] 6144  
3120.w4 3120z6 [0, 1, 0, -1840, 834260] [4] 12288  
3120.w5 3120z2 [0, 1, 0, -1040, -5100] [2, 2] 3072  
3120.w6 3120z1 [0, 1, 0, 240, -492] [2] 1536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3120.w have rank \(1\).

Modular form 3120.2.a.w

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.