Properties

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

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Show commands: SageMath
E = EllipticCurve("cc1")
 
E.isogeny_class()
 

Elliptic curves in class 155526cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155526.bb2 155526cc1 \([1, 0, 1, -2372312, 12578150]\) \(6967871/4032\) \(854396159776832683584\) \([2]\) \(7630848\) \(2.7059\) \(\Gamma_0(N)\)-optimal
155526.bb1 155526cc2 \([1, 0, 1, -26219632, 51522789350]\) \(9407293631/31752\) \(6728369758242557383224\) \([2]\) \(15261696\) \(3.0525\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 155526.2.a.cc

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