Properties

Label 336.d
Number of curves $6$
Conductor $336$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("336.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 336.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
336.d1 336d3 [0, 1, 0, -21504, -1220940] [2] 384  
336.d2 336d5 [0, 1, 0, -14624, 669300] [8] 768  
336.d3 336d4 [0, 1, 0, -1664, -9804] [2, 4] 384  
336.d4 336d2 [0, 1, 0, -1344, -19404] [2, 2] 192  
336.d5 336d1 [0, 1, 0, -64, -460] [2] 96 \(\Gamma_0(N)\)-optimal
336.d6 336d6 [0, 1, 0, 6176, -69388] [4] 768  

Rank

sage: E.rank()
 

The elliptic curves in class 336.d have rank \(0\).

Modular form 336.2.a.d

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} + q^{7} + q^{9} + 4q^{11} + 6q^{13} - 2q^{15} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.