Properties

Label 117600.u
Number of curves $4$
Conductor $117600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 117600.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117600.u1 117600fh4 \([0, -1, 0, -461008, 120607012]\) \(11512557512/2835\) \(2668279320000000\) \([2]\) \(1179648\) \(1.9479\)  
117600.u2 117600fh3 \([0, -1, 0, -216008, -37540488]\) \(1184287112/36015\) \(33897029880000000\) \([2]\) \(1179648\) \(1.9479\)  
117600.u3 117600fh1 \([0, -1, 0, -32258, 1414512]\) \(31554496/11025\) \(1297080225000000\) \([2, 2]\) \(589824\) \(1.6014\) \(\Gamma_0(N)\)-optimal
117600.u4 117600fh2 \([0, -1, 0, 96367, 9775137]\) \(13144256/13125\) \(-98825160000000000\) \([2]\) \(1179648\) \(1.9479\)  

Rank

sage: E.rank()
 

The elliptic curves in class 117600.u have rank \(1\).

Complex multiplication

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

Modular form 117600.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 4 q^{11} + 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 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.