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Properties

Label 39600dt
Number of curves $6$
Conductor $39600$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dt1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 39600dt have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 2 T + 7 T^{2}\) 1.7.ac
\(13\) \( 1 + T + 13 T^{2}\) 1.13.b
\(17\) \( 1 - 4 T + 17 T^{2}\) 1.17.ae
\(19\) \( 1 + T + 19 T^{2}\) 1.19.b
\(23\) \( 1 + T + 23 T^{2}\) 1.23.b
\(29\) \( 1 - 9 T + 29 T^{2}\) 1.29.aj
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 39600dt do not have complex multiplication.

Modular form 39600.2.a.dt

Copy content sage:E.q_eigenform(10)
 
\(q + q^{11} - 6 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 39600dt

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39600.cp6 39600dt1 \([0, 0, 0, 917925, 32170250]\) \(1833318007919/1070530560\) \(-49946673807360000000\) \([2]\) \(884736\) \(2.4692\) \(\Gamma_0(N)\)-optimal
39600.cp5 39600dt2 \([0, 0, 0, -3690075, 257962250]\) \(119102750067601/68309049600\) \(3187027018137600000000\) \([2, 2]\) \(1769472\) \(2.8158\)  
39600.cp3 39600dt3 \([0, 0, 0, -38538075, -91705909750]\) \(135670761487282321/643043610000\) \(30001842668160000000000\) \([2, 2]\) \(3538944\) \(3.1624\)  
39600.cp2 39600dt4 \([0, 0, 0, -42570075, 106672522250]\) \(182864522286982801/463015182960\) \(21602436376181760000000\) \([4]\) \(3538944\) \(3.1624\)  
39600.cp4 39600dt5 \([0, 0, 0, -18738075, -185815309750]\) \(-15595206456730321/310672490129100\) \(-14494735699463289600000000\) \([2]\) \(7077888\) \(3.5089\)  
39600.cp1 39600dt6 \([0, 0, 0, -615906075, -5883284317750]\) \(553808571467029327441/12529687500\) \(584585100000000000000\) \([2]\) \(7077888\) \(3.5089\)