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Properties

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

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 55506g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55506.j2 55506g1 \([1, 1, 0, 41, -95]\) \(300763/396\) \(-9658044\) \([2]\) \(17920\) \(0.026130\) \(\Gamma_0(N)\)-optimal
55506.j1 55506g2 \([1, 1, 0, -249, -1197]\) \(70444997/19602\) \(478073178\) \([2]\) \(35840\) \(0.37270\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 55506.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9} - 2 q^{10} - q^{11} - q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} + 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.