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Properties

Label 109200da
Number of curves $4$
Conductor $109200$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("da1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 109200da have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1 - T\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 2 T + 11 T^{2}\) 1.11.ac
\(17\) \( 1 - T + 17 T^{2}\) 1.17.ab
\(19\) \( 1 - 2 T + 19 T^{2}\) 1.19.ac
\(23\) \( 1 + 5 T + 23 T^{2}\) 1.23.f
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 109200da do not have complex multiplication.

Modular form 109200.2.a.da

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 4 q^{11} - q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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 109200da

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
109200.f4 109200da1 \([0, -1, 0, -288017408, -952985714688]\) \(41285728533151645510969/17760741842188800000\) \(1136687477900083200000000000\) \([2]\) \(66355200\) \(3.8879\) \(\Gamma_0(N)\)-optimal
109200.f2 109200da2 \([0, -1, 0, -3943825408, -95287455346688]\) \(105997782562506306791694649/51649016225625000000\) \(3305537038440000000000000000\) \([2, 2]\) \(132710400\) \(4.2344\)  
109200.f3 109200da3 \([0, -1, 0, -3286753408, -128080604722688]\) \(-61354313914516350666047929/75227254486083984375000\) \(-4814544287109375000000000000000\) \([2]\) \(265420800\) \(4.5810\)  
109200.f1 109200da4 \([0, -1, 0, -63093825408, -6099958855346688]\) \(434014578033107719741685694649/103121648659575000\) \(6599785514212800000000000\) \([2]\) \(265420800\) \(4.5810\)