Properties

Label 13552.w
Number of curves $6$
Conductor $13552$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 13552.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13552.w1 13552ba6 \([0, -1, 0, -5286288, -4676390464]\) \(2251439055699625/25088\) \(182046402019328\) \([2]\) \(207360\) \(2.3052\)  
13552.w2 13552ba5 \([0, -1, 0, -330128, -73109056]\) \(-548347731625/1835008\) \(-13315393976270848\) \([2]\) \(103680\) \(1.9586\)  
13552.w3 13552ba4 \([0, -1, 0, -68768, -5666560]\) \(4956477625/941192\) \(6829584550756352\) \([2]\) \(69120\) \(1.7559\)  
13552.w4 13552ba2 \([0, -1, 0, -20368, 1124928]\) \(128787625/98\) \(711118757888\) \([2]\) \(23040\) \(1.2066\)  
13552.w5 13552ba1 \([0, -1, 0, -1008, 25280]\) \(-15625/28\) \(-203176787968\) \([2]\) \(11520\) \(0.86001\) \(\Gamma_0(N)\)-optimal
13552.w6 13552ba3 \([0, -1, 0, 8672, -524544]\) \(9938375/21952\) \(-159290601766912\) \([2]\) \(34560\) \(1.4093\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13552.w have rank \(0\).

Complex multiplication

The elliptic curves in class 13552.w do not have complex multiplication.

Modular form 13552.2.a.w

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.