↑

Properties

Label 155526cd
Number of curves $2$
Conductor $155526$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 155526cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155526.bc1 155526cd1 \([1, 0, 1, -55639967, 147371907890]\) \(3188856056959/274710528\) \(1641060831167273579986944\) \([2]\) \(39739392\) \(3.3874\) \(\Gamma_0(N)\)-optimal
155526.bc2 155526cd2 \([1, 0, 1, 60486113, 681784128050]\) \(4096768048001/35984932992\) \(-214966148095169344653446016\) \([2]\) \(79478784\) \(3.7340\)  

Rank

sage: E.rank()
 

The elliptic curves in class 155526cd have rank \(0\).

Complex multiplication

The elliptic curves in class 155526cd do not have complex multiplication.

Modular form 155526.2.a.cd

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{8} + q^{9} + 2 q^{10} + 6 q^{11} + q^{12} - 6 q^{13} - 2 q^{15} + q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.