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Properties

Label 142296.dl
Number of curves $6$
Conductor $142296$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dl1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 142296.dl have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(7\)\(1\)
\(11\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 8 T + 23 T^{2}\) 1.23.i
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 142296.dl do not have complex multiplication.

Modular form 142296.2.a.dl

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 142296.dl

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142296.dl1 142296cn6 \([0, 1, 0, -2278712, -1324739088]\) \(3065617154/9\) \(3841641309800448\) \([2]\) \(1966080\) \(2.2197\)  
142296.dl2 142296cn3 \([0, 1, 0, -381432, 90536928]\) \(28756228/3\) \(640273551633408\) \([2]\) \(983040\) \(1.8731\)  
142296.dl3 142296cn4 \([0, 1, 0, -144272, -20169360]\) \(1556068/81\) \(17287385894102016\) \([2, 2]\) \(983040\) \(1.8731\)  
142296.dl4 142296cn2 \([0, 1, 0, -25692, 1175040]\) \(35152/9\) \(480205163725056\) \([2, 2]\) \(491520\) \(1.5266\)  
142296.dl5 142296cn1 \([0, 1, 0, 3953, 119678]\) \(2048/3\) \(-10004274244272\) \([2]\) \(245760\) \(1.1800\) \(\Gamma_0(N)\)-optimal
142296.dl6 142296cn5 \([0, 1, 0, 92888, -79743952]\) \(207646/6561\) \(-2800556514844526592\) \([2]\) \(1966080\) \(2.2197\)