Properties

Label 155526cy
Number of curves $4$
Conductor $155526$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cy1")
 
E.isogeny_class()
 

Elliptic curves in class 155526cy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155526.h3 155526cy1 \([1, 1, 0, -920735, 355219509]\) \(-4956477625/268272\) \(-4672298740340497392\) \([2]\) \(3041280\) \(2.3408\) \(\Gamma_0(N)\)-optimal
155526.h2 155526cy2 \([1, 1, 0, -14918075, 22171473633]\) \(21081759765625/57132\) \(995026583591031852\) \([2]\) \(6082560\) \(2.6874\)  
155526.h4 155526cy3 \([1, 1, 0, 4911490, 730114932]\) \(752329532375/448524288\) \(-7811622032245327392768\) \([2]\) \(9123840\) \(2.8901\)  
155526.h1 155526cy4 \([1, 1, 0, -19972670, 5861228724]\) \(50591419971625/28422890688\) \(495020860762129679103168\) \([2]\) \(18247680\) \(3.2367\)  

Rank

sage: E.rank()
 

The elliptic curves in class 155526cy have rank \(1\).

Complex multiplication

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

Modular form 155526.2.a.cy

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.