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Properties

Label 142800dm
Number of curves $6$
Conductor $142800$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dm1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 142800dm have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1 - T\)
\(17\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + T + 11 T^{2}\) 1.11.b
\(13\) \( 1 - 4 T + 13 T^{2}\) 1.13.ae
\(19\) \( 1 + 2 T + 19 T^{2}\) 1.19.c
\(23\) \( 1 + 3 T + 23 T^{2}\) 1.23.d
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 142800dm do not have complex multiplication.

Modular form 142800.2.a.dm

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - 4 q^{11} + 2 q^{13} - q^{17} - 4 q^{19} + O(q^{20})\) 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 142800dm

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142800.ct5 142800dm1 \([0, -1, 0, -28097608, -57244982288]\) \(38331145780597164097/55468445663232\) \(3549980522446848000000\) \([2]\) \(11796480\) \(3.0373\) \(\Gamma_0(N)\)-optimal
142800.ct4 142800dm2 \([0, -1, 0, -36289608, -21134646288]\) \(82582985847542515777/44772582831427584\) \(2865445301211365376000000\) \([2, 2]\) \(23592960\) \(3.3838\)  
142800.ct2 142800dm3 \([0, -1, 0, -343617608, 2435030729712]\) \(70108386184777836280897/552468975892674624\) \(35358014457131175936000000\) \([2, 2]\) \(47185920\) \(3.7304\)  
142800.ct6 142800dm4 \([0, -1, 0, 139966392, -166369590288]\) \(4738217997934888496063/2928751705237796928\) \(-187440109135219003392000000\) \([2]\) \(47185920\) \(3.7304\)  
142800.ct1 142800dm5 \([0, -1, 0, -5487441608, 156461696585712]\) \(285531136548675601769470657/17941034271597192\) \(1148226193382220288000000\) \([2]\) \(94371840\) \(4.0770\)  
142800.ct3 142800dm6 \([0, -1, 0, -117041608, 5598031689712]\) \(-2770540998624539614657/209924951154647363208\) \(-13435196873897431245312000000\) \([2]\) \(94371840\) \(4.0770\)