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Properties

Label 346560.dy
Number of curves $4$
Conductor $346560$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dy1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 346560.dy have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(19\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 2 T + 7 T^{2}\) 1.7.c
\(11\) \( 1 - 6 T + 11 T^{2}\) 1.11.ag
\(13\) \( 1 + 4 T + 13 T^{2}\) 1.13.e
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 29 T^{2}\) 1.29.a
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 346560.dy do not have complex multiplication.

Modular form 346560.2.a.dy

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 2 q^{7} + q^{9} + 6 q^{11} - 4 q^{13} - q^{15} - 6 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 346560.dy

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.dy1 346560dy4 \([0, -1, 0, -10702489505, 272128525001025]\) \(10993009831928446009969/3767761230468750000\) \(46467028480176000000000000000000\) \([2]\) \(1194393600\) \(4.7783\)  
346560.dy2 346560dy2 \([0, -1, 0, -9587952545, 361360539841857]\) \(7903870428425797297009/886464000000\) \(10932579167052496896000000\) \([2]\) \(398131200\) \(4.2290\)  
346560.dy3 346560dy1 \([0, -1, 0, -597724065, 5676534396225]\) \(-1914980734749238129/20440940544000\) \(-252093938102724005462016000\) \([2]\) \(199065600\) \(3.8824\) \(\Gamma_0(N)\)-optimal
346560.dy4 346560dy3 \([0, -1, 0, 1975137375, 29547205702977]\) \(69096190760262356111/70568821500000000\) \(-870310839215519563776000000000\) \([2]\) \(597196800\) \(4.4317\)