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Properties

Label 179520.gd
Number of curves $8$
Conductor $179520$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("gd1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 179520.gd have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(11\)\(1 - T\)
\(17\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 4 T + 7 T^{2}\) 1.7.ae
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 179520.gd do not have complex multiplication.

Modular form 179520.2.a.gd

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 4 q^{7} + q^{9} + q^{11} - 2 q^{13} - q^{15} - q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 179520.gd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
179520.gd1 179520bv7 \([0, 1, 0, -12879134881, 562567756120799]\) \(901247067798311192691198986281/552431869440\) \(144816699982479360\) \([2]\) \(127401984\) \(4.0005\)  
179520.gd2 179520bv8 \([0, 1, 0, -810352801, 8665841992415]\) \(224494757451893010998773801/6152490825146276160000\) \(1612838554867145417687040000\) \([2]\) \(127401984\) \(4.0005\)  
179520.gd3 179520bv6 \([0, 1, 0, -804946081, 8789916484319]\) \(220031146443748723000125481/172266701724057600\) \(45158682256751355494400\) \([2, 2]\) \(63700992\) \(3.6539\)  
179520.gd4 179520bv4 \([0, 1, 0, -159034081, 771320361119]\) \(1696892787277117093383481/1440538624914939000\) \(377628557289701769216000\) \([2]\) \(42467328\) \(3.4512\)  
179520.gd5 179520bv5 \([0, 1, 0, -104152801, -404787487585]\) \(476646772170172569823801/5862293314453125000\) \(1536765018624000000000000\) \([2]\) \(42467328\) \(3.4512\)  
179520.gd6 179520bv3 \([0, 1, 0, -49971361, 139265147615]\) \(-52643812360427830814761/1504091705903677440\) \(-394288616152413618831360\) \([2]\) \(31850496\) \(3.3074\)  
179520.gd7 179520bv2 \([0, 1, 0, -12154081, 6281193119]\) \(757443433548897303481/373234243041000000\) \(97841117407739904000000\) \([2, 2]\) \(21233664\) \(3.1046\)  
179520.gd8 179520bv1 \([0, 1, 0, 2775839, 754136735]\) \(9023321954633914439/6156756739584000\) \(-1613956838741508096000\) \([2]\) \(10616832\) \(2.7581\) \(\Gamma_0(N)\)-optimal