Properties

Label 155232x
Number of curves $4$
Conductor $155232$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 155232x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155232.be3 155232x1 \([0, 0, 0, -15141, -624260]\) \(69934528/9801\) \(53798000122944\) \([2, 2]\) \(393216\) \(1.3609\) \(\Gamma_0(N)\)-optimal
155232.be2 155232x2 \([0, 0, 0, -63651, 5555914]\) \(649461896/72171\) \(3169191279969792\) \([2]\) \(786432\) \(1.7075\)  
155232.be4 155232x3 \([0, 0, 0, 24549, -3346994]\) \(37259704/131769\) \(-5786273791001088\) \([2]\) \(786432\) \(1.7075\)  
155232.be1 155232x4 \([0, 0, 0, -233436, -43410080]\) \(4004529472/99\) \(34778505129984\) \([2]\) \(786432\) \(1.7075\)  

Rank

sage: E.rank()
 

The elliptic curves in class 155232x have rank \(0\).

Complex multiplication

The elliptic curves in class 155232x do not have complex multiplication.

Modular form 155232.2.a.x

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - q^{11} + 6 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.