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Properties

Label 55506h
Number of curves $2$
Conductor $55506$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 55506h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55506.d2 55506h1 \([1, 1, 0, -16196836, 27470238160]\) \(-32391594523133/3737124864\) \(-54215015932097583906816\) \([2]\) \(6859776\) \(3.0987\) \(\Gamma_0(N)\)-optimal
55506.d1 55506h2 \([1, 1, 0, -265940196, 1669133240784]\) \(143381687390091773/1625868288\) \(23586708591552220342272\) \([2]\) \(13719552\) \(3.4452\)  

Rank

sage: E.rank()
 

The elliptic curves in class 55506h have rank \(0\).

Complex multiplication

The elliptic curves in class 55506h do not have complex multiplication.

Modular form 55506.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + 2 q^{10} - q^{11} - q^{12} + 4 q^{14} + 2 q^{15} + q^{16} + 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.