Properties

Label 117600.t
Number of curves $4$
Conductor $117600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 117600.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117600.t1 117600bb4 \([0, -1, 0, -1372408, 619289812]\) \(303735479048/105\) \(98825160000000\) \([2]\) \(1769472\) \(2.0413\)  
117600.t2 117600bb3 \([0, -1, 0, -178033, -14372063]\) \(82881856/36015\) \(271176239040000000\) \([2]\) \(1769472\) \(2.0413\)  
117600.t3 117600bb1 \([0, -1, 0, -86158, 9607312]\) \(601211584/11025\) \(1297080225000000\) \([2, 2]\) \(884736\) \(1.6947\) \(\Gamma_0(N)\)-optimal
117600.t4 117600bb2 \([0, -1, 0, -408, 27786312]\) \(-8/354375\) \(-333534915000000000\) \([2]\) \(1769472\) \(2.0413\)  

Rank

sage: E.rank()
 

The elliptic curves in class 117600.t have rank \(0\).

Complex multiplication

The elliptic curves in class 117600.t do not have complex multiplication.

Modular form 117600.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 4q^{11} + 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.