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Properties

Label 40560bv
Number of curves $8$
Conductor $40560$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 40560bv have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 40560bv do not have complex multiplication.

Modular form 40560.2.a.bv

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 40560bv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40560.q8 40560bv1 \([0, -1, 0, 4000, -300288]\) \(357911/2160\) \(-42704516874240\) \([2]\) \(110592\) \(1.2973\) \(\Gamma_0(N)\)-optimal
40560.q6 40560bv2 \([0, -1, 0, -50080, -3891200]\) \(702595369/72900\) \(1441277444505600\) \([2, 2]\) \(221184\) \(1.6439\)  
40560.q7 40560bv3 \([0, -1, 0, -36560, 8817600]\) \(-273359449/1536000\) \(-30367656443904000\) \([2]\) \(331776\) \(1.8466\)  
40560.q5 40560bv4 \([0, -1, 0, -185280, 26501760]\) \(35578826569/5314410\) \(105069125704458240\) \([2]\) \(442368\) \(1.9905\)  
40560.q4 40560bv5 \([0, -1, 0, -780160, -264967808]\) \(2656166199049/33750\) \(667258076160000\) \([2]\) \(442368\) \(1.9905\)  
40560.q3 40560bv6 \([0, -1, 0, -901840, 329317312]\) \(4102915888729/9000000\) \(177935486976000000\) \([2, 2]\) \(663552\) \(2.1932\)  
40560.q1 40560bv7 \([0, -1, 0, -14421840, 21085221312]\) \(16778985534208729/81000\) \(1601419382784000\) \([2]\) \(1327104\) \(2.5398\)  
40560.q2 40560bv8 \([0, -1, 0, -1226320, 71550400]\) \(10316097499609/5859375000\) \(115843416000000000000\) \([2]\) \(1327104\) \(2.5398\)