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Properties

Label 158400ly
Number of curves $6$
Conductor $158400$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ly1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 158400ly have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1\)
\(11\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 2 T + 7 T^{2}\) 1.7.ac
\(13\) \( 1 - T + 13 T^{2}\) 1.13.ab
\(17\) \( 1 + 4 T + 17 T^{2}\) 1.17.e
\(19\) \( 1 + 3 T + 19 T^{2}\) 1.19.d
\(23\) \( 1 + T + 23 T^{2}\) 1.23.b
\(29\) \( 1 - 3 T + 29 T^{2}\) 1.29.ad
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 158400ly do not have complex multiplication.

Modular form 158400.2.a.ly

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 158400ly

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158400.gu5 158400ly1 \([0, 0, 0, 71700, -28658000]\) \(13651919/126720\) \(-378383892480000000\) \([2]\) \(1179648\) \(2.0541\) \(\Gamma_0(N)\)-optimal
158400.gu4 158400ly2 \([0, 0, 0, -1080300, -399602000]\) \(46694890801/3920400\) \(11706251673600000000\) \([2, 2]\) \(2359296\) \(2.4007\)  
158400.gu3 158400ly3 \([0, 0, 0, -3672300, 2249422000]\) \(1834216913521/329422500\) \(983650314240000000000\) \([2, 2]\) \(4718592\) \(2.7473\)  
158400.gu2 158400ly4 \([0, 0, 0, -16920300, -26789042000]\) \(179415687049201/1443420\) \(4310029025280000000\) \([2]\) \(4718592\) \(2.7473\)  
158400.gu1 158400ly5 \([0, 0, 0, -55944300, 161051758000]\) \(6484907238722641/283593750\) \(846806400000000000000\) \([2]\) \(9437184\) \(3.0938\)  
158400.gu6 158400ly6 \([0, 0, 0, 7127700, 12984622000]\) \(13411719834479/32153832150\) \(-96010828338585600000000\) \([2]\) \(9437184\) \(3.0938\)