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Properties

Label 29400.ce
Number of curves $6$
Conductor $29400$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ce1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 29400.ce have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 - 8 T + 23 T^{2}\) 1.23.ai
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 29400.ce do not have complex multiplication.

Modular form 29400.2.a.ce

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 29400.ce

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29400.ce1 29400n6 \([0, -1, 0, -470808, 124497612]\) \(3065617154/9\) \(33882912000000\) \([2]\) \(196608\) \(1.8255\)  
29400.ce2 29400n4 \([0, -1, 0, -78808, -8488388]\) \(28756228/3\) \(5647152000000\) \([2]\) \(98304\) \(1.4789\)  
29400.ce3 29400n3 \([0, -1, 0, -29808, 1899612]\) \(1556068/81\) \(152473104000000\) \([2, 2]\) \(98304\) \(1.4789\)  
29400.ce4 29400n2 \([0, -1, 0, -5308, -109388]\) \(35152/9\) \(4235364000000\) \([2, 2]\) \(49152\) \(1.1323\)  
29400.ce5 29400n1 \([0, -1, 0, 817, -11388]\) \(2048/3\) \(-88236750000\) \([2]\) \(24576\) \(0.78575\) \(\Gamma_0(N)\)-optimal
29400.ce6 29400n5 \([0, -1, 0, 19192, 7485612]\) \(207646/6561\) \(-24700642848000000\) \([2]\) \(196608\) \(1.8255\)