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Properties

Label 283920.dk
Number of curves $8$
Conductor $283920$
CM no
Rank $2$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dk1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 283920.dk have rank \(2\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1 - T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 + 4 T + 19 T^{2}\) 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 283920.dk do not have complex multiplication.

Modular form 283920.2.a.dk

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} - q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 283920.dk

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.dk1 283920dk8 \([0, -1, 0, -17443560, -17636072208]\) \(29689921233686449/10380965400750\) \(205238014873717582848000\) \([2]\) \(31850496\) \(3.1746\)  
283920.dk2 283920dk5 \([0, -1, 0, -15577800, -23659848720]\) \(21145699168383889/2593080\) \(51266772507525120\) \([2]\) \(10616832\) \(2.6253\)  
283920.dk3 283920dk6 \([0, -1, 0, -7303560, 7397559792]\) \(2179252305146449/66177562500\) \(1308370756702464000000\) \([2, 2]\) \(15925248\) \(2.8281\)  
283920.dk4 283920dk3 \([0, -1, 0, -7249480, 7515324400]\) \(2131200347946769/2058000\) \(40687914688512000\) \([2]\) \(7962624\) \(2.4815\)  
283920.dk5 283920dk2 \([0, -1, 0, -976200, -367376400]\) \(5203798902289/57153600\) \(1129961516492390400\) \([2, 2]\) \(5308416\) \(2.2788\)  
283920.dk6 283920dk4 \([0, -1, 0, -219080, -923405328]\) \(-58818484369/18600435000\) \(-367741939965603840000\) \([2]\) \(10616832\) \(2.6253\)  
283920.dk7 283920dk1 \([0, -1, 0, -110920, 5040112]\) \(7633736209/3870720\) \(76526494238638080\) \([2]\) \(2654208\) \(1.9322\) \(\Gamma_0(N)\)-optimal
283920.dk8 283920dk7 \([0, -1, 0, 1971160, 24893391600]\) \(42841933504271/13565917968750\) \(-268206468894000000000000\) \([2]\) \(31850496\) \(3.1746\)