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Properties

Label 29040.dg
Number of curves $6$
Conductor $29040$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dg1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 29040.dg 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 \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 29040.dg do not have complex multiplication.

Modular form 29040.2.a.dg

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 2 q^{13} + q^{15} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 29040.dg

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29040.dg1 29040bg4 \([0, 1, 0, -6388840, 6213443300]\) \(15897679904620804/2475\) \(4489844198400\) \([4]\) \(491520\) \(2.2743\)  
29040.dg2 29040bg6 \([0, 1, 0, -3388040, -2355457260]\) \(1185450336504002/26043266205\) \(94489056709419018240\) \([2]\) \(983040\) \(2.6209\)  
29040.dg3 29040bg3 \([0, 1, 0, -459840, 65578500]\) \(5927735656804/2401490025\) \(4356491335863321600\) \([2, 2]\) \(491520\) \(2.2743\)  
29040.dg4 29040bg2 \([0, 1, 0, -399340, 96965900]\) \(15529488955216/6125625\) \(2778091097760000\) \([2, 2]\) \(245760\) \(1.9278\)  
29040.dg5 29040bg1 \([0, 1, 0, -21215, 1980900]\) \(-37256083456/38671875\) \(-1096153368750000\) \([2]\) \(122880\) \(1.5812\) \(\Gamma_0(N)\)-optimal
29040.dg6 29040bg5 \([0, 1, 0, 1500360, 478788660]\) \(102949393183198/86815346805\) \(-314979701967283415040\) \([2]\) \(983040\) \(2.6209\)