Properties

Label 152880fq
Number of curves $4$
Conductor $152880$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fq1")
 
E.isogeny_class()
 

Elliptic curves in class 152880fq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152880.gk3 152880fq1 \([0, 1, 0, -5455, 152900]\) \(9538484224/26325\) \(49553758800\) \([2]\) \(221184\) \(0.92513\) \(\Gamma_0(N)\)-optimal
152880.gk2 152880fq2 \([0, 1, 0, -7660, 15308]\) \(1650587344/950625\) \(28631060640000\) \([2, 2]\) \(442368\) \(1.2717\)  
152880.gk4 152880fq3 \([0, 1, 0, 30560, 152900]\) \(26198797244/15234375\) \(-1835324400000000\) \([2]\) \(884736\) \(1.6183\)  
152880.gk1 152880fq4 \([0, 1, 0, -81160, -8892892]\) \(490757540836/2142075\) \(258061293235200\) \([2]\) \(884736\) \(1.6183\)  

Rank

sage: E.rank()
 

The elliptic curves in class 152880fq have rank \(0\).

Complex multiplication

The elliptic curves in class 152880fq do not have complex multiplication.

Modular form 152880.2.a.fq

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