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Properties

Label 152880.hj
Number of curves $8$
Conductor $152880$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("hj1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 152880.hj have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 - T\)
\(7\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 + 4 T + 19 T^{2}\) 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 152880.hj do not have complex multiplication.

Modular form 152880.2.a.hj

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - q^{13} + q^{15} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 152880.hj

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152880.hj1 152880bb8 \([0, 1, 0, -1776291960, -28810872974892]\) \(1286229821345376481036009/247265484375000000\) \(119154839434176000000000000\) \([2]\) \(95551488\) \(4.0040\)  
152880.hj2 152880bb7 \([0, 1, 0, -781301880, 8141638214100]\) \(109454124781830273937129/3914078300576808000\) \(1886156382144761382469632000\) \([2]\) \(95551488\) \(4.0040\)  
152880.hj3 152880bb4 \([0, 1, 0, -774469320, 8295468643188]\) \(106607603143751752938169/5290068420\) \(2549232679094599680\) \([2]\) \(31850496\) \(3.4547\)  
152880.hj4 152880bb6 \([0, 1, 0, -122741880, -349307577900]\) \(424378956393532177129/136231857216000000\) \(65648811088302833664000000\) \([2, 2]\) \(47775744\) \(3.6575\)  
152880.hj5 152880bb5 \([0, 1, 0, -53910600, 98287312500]\) \(35958207000163259449/12145729518877500\) \(5852909290153652213760000\) \([2]\) \(31850496\) \(3.4547\)  
152880.hj6 152880bb2 \([0, 1, 0, -48406920, 129590042868]\) \(26031421522845051769/5797789779600\) \(2793898679419536998400\) \([2, 2]\) \(15925248\) \(3.1082\)  
152880.hj7 152880bb1 \([0, 1, 0, -2684040, 2498725620]\) \(-4437543642183289/3033210136320\) \(-1461674554687126241280\) \([2]\) \(7962624\) \(2.7616\) \(\Gamma_0(N)\)-optimal
152880.hj8 152880bb3 \([0, 1, 0, 21765000, -37230519852]\) \(2366200373628880151/2612420149248000\) \(-1258899939896844091392000\) \([2]\) \(23887872\) \(3.3109\)