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Properties

Label 116160.er
Number of curves $4$
Conductor $116160$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("er1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 116160.er have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(11\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 4 T + 7 T^{2}\) 1.7.ae
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 116160.er do not have complex multiplication.

Modular form 116160.2.a.er

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 4 q^{7} + q^{9} + 2 q^{13} - q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 116160.er

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116160.er1 116160hc4 \([0, -1, 0, -14194024225, -650840397282623]\) \(680995599504466943307169/52207031250000000\) \(24245158671360000000000000000\) \([2]\) \(206438400\) \(4.4947\)  
116160.er2 116160hc2 \([0, -1, 0, -946208545, -8737318214975]\) \(201738262891771037089/45727545600000000\) \(21236059055241717350400000000\) \([2, 2]\) \(103219200\) \(4.1482\)  
116160.er3 116160hc1 \([0, -1, 0, -311820065, 2002498118337]\) \(7220044159551112609/448454983680000\) \(208264327159644023685120000\) \([2]\) \(51609600\) \(3.8016\) \(\Gamma_0(N)\)-optimal
116160.er4 116160hc3 \([0, -1, 0, 2151391455, -53992634694975]\) \(2371297246710590562911/4084000833203280000\) \(-1896626677368864353833451520000\) \([2]\) \(206438400\) \(4.4947\)