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Properties

Label 171600.ea
Number of curves $4$
Conductor $171600$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ea1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 171600.ea have rank \(0\).

L-function data

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

Complex multiplication

The elliptic curves in class 171600.ea do not have complex multiplication.

Modular form 171600.2.a.ea

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{7} + q^{9} + q^{11} + q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 171600.ea

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
171600.ea1 171600ex3 \([0, -1, 0, -5306808, 4676576112]\) \(258252149810350513/1938176193096\) \(124043276358144000000\) \([2]\) \(7077888\) \(2.6857\)  
171600.ea2 171600ex2 \([0, -1, 0, -554808, -37407888]\) \(295102348042033/161237583936\) \(10319205371904000000\) \([2, 2]\) \(3538944\) \(2.3391\)  
171600.ea3 171600ex1 \([0, -1, 0, -426808, -107039888]\) \(134351465835313/205590528\) \(13157793792000000\) \([2]\) \(1769472\) \(1.9926\) \(\Gamma_0(N)\)-optimal
171600.ea4 171600ex4 \([0, -1, 0, 2149192, -296991888]\) \(17154149157653327/10519679024712\) \(-673259457581568000000\) \([2]\) \(7077888\) \(2.6857\)