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Properties

Label 283920dp
Number of curves $4$
Conductor $283920$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dp1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 283920dp have rank \(0\).

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
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 8 T + 23 T^{2}\) 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 283920dp do not have complex multiplication.

Modular form 283920.2.a.dp

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} - q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 283920dp

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.dp3 283920dp1 \([0, -1, 0, -861051000, 7726654950000]\) \(3571003510905229697089/762141946675200000\) \(15068010936276481789132800000\) \([2]\) \(185794560\) \(4.1212\) \(\Gamma_0(N)\)-optimal
283920.dp2 283920dp2 \([0, -1, 0, -4405237880, -105778056394128]\) \(478202393398338853167169/32244226560000000000\) \(637488017235341475840000000000\) \([2, 2]\) \(371589120\) \(4.4678\)  
283920.dp4 283920dp3 \([0, -1, 0, 3783772040, -453987860608400]\) \(303025056761573589385151/4678857421875000000000\) \(-92503863761400000000000000000000\) \([2]\) \(743178240\) \(4.8143\)  
283920.dp1 283920dp4 \([0, -1, 0, -69301237880, -7021926485194128]\) \(1861772567578966373029167169/9401133413380800000\) \(185866139115139751392051200000\) \([2]\) \(743178240\) \(4.8143\)