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Properties

Label 155526dc
Number of curves $2$
Conductor $155526$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dc1")
 
E.isogeny_class()
 

Elliptic curves in class 155526dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155526.l1 155526dc1 \([1, 1, 0, -1135509, -430142355]\) \(3188856056959/274710528\) \(13948786909937811456\) \([2]\) \(5677056\) \(2.4145\) \(\Gamma_0(N)\)-optimal
155526.l2 155526dc2 \([1, 1, 0, 1234411, -1987179795]\) \(4096768048001/35984932992\) \(-1827182110304119411584\) \([2]\) \(11354112\) \(2.7611\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 155526.2.a.dc

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.