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Properties

Label 116160.bj
Number of curves $6$
Conductor $116160$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bj1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 116160.bj have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 + T\)
\(11\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(13\) \( 1 - 6 T + 13 T^{2}\) 1.13.ag
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 116160.bj do not have complex multiplication.

Modular form 116160.2.a.bj

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + 6 q^{13} + q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 116160.bj

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116160.bj1 116160fc6 \([0, -1, 0, -1324882401, -18561102495615]\) \(553808571467029327441/12529687500\) \(5818838081126400000000\) \([2]\) \(35389440\) \(3.7004\)  
116160.bj2 116160fc4 \([0, -1, 0, -91572961, 336578381185]\) \(182864522286982801/463015182960\) \(215026143209665478000640\) \([2]\) \(17694720\) \(3.3539\)  
116160.bj3 116160fc3 \([0, -1, 0, -82899681, -289301115519]\) \(135670761487282321/643043610000\) \(298632080464336650240000\) \([2, 2]\) \(17694720\) \(3.3539\)  
116160.bj4 116160fc5 \([0, -1, 0, -40307681, -586226984319]\) \(-15595206456730321/310672490129100\) \(-144277574067315939763814400\) \([2]\) \(35389440\) \(3.7004\)  
116160.bj5 116160fc2 \([0, -1, 0, -7937761, 816507265]\) \(119102750067601/68309049600\) \(31723001798570960486400\) \([2, 2]\) \(8847360\) \(3.0073\)  
116160.bj6 116160fc1 \([0, -1, 0, 1974559, 100837761]\) \(1833318007919/1070530560\) \(-497158767091164119040\) \([2]\) \(4423680\) \(2.6607\) \(\Gamma_0(N)\)-optimal