Properties

Label 152592dc
Number of curves $4$
Conductor $152592$
CM no
Rank $1$
Graph

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

Elliptic curves in class 152592dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152592.g3 152592dc1 \([0, -1, 0, -8268964, -9149428640]\) \(10119139303540048/85833\) \(530380789754112\) \([2]\) \(3538944\) \(2.4117\) \(\Gamma_0(N)\)-optimal
152592.g2 152592dc2 \([0, -1, 0, -8274744, -9135991296]\) \(2535093488117092/7367303889\) \(182096697307858781184\) \([2, 2]\) \(7077888\) \(2.7582\)  
152592.g1 152592dc3 \([0, -1, 0, -11708064, -827356896]\) \(3590504967602306/2071799959977\) \(102416823271714971469824\) \([2]\) \(14155776\) \(3.1048\)  
152592.g4 152592dc4 \([0, -1, 0, -4933904, -16584728160]\) \(-268702931670626/2248659199809\) \(-111159637182207025809408\) \([2]\) \(14155776\) \(3.1048\)  

Rank

sage: E.rank()
 

The elliptic curves in class 152592dc have rank \(1\).

Complex multiplication

The elliptic curves in class 152592dc do not have complex multiplication.

Modular form 152592.2.a.dc

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} - 4 q^{7} + q^{9} - q^{11} + 2 q^{13} + 2 q^{15} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.