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Properties

Label 145200.dj
Number of curves $6$
Conductor $145200$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dj1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 145200.dj have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(11\)\(1\)
 
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.ac
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 145200.dj do not have complex multiplication.

Modular form 145200.2.a.dj

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 6 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 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 145200.dj

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145200.dj1 145200fs6 \([0, -1, 0, -8280515008, -290021366751488]\) \(553808571467029327441/12529687500\) \(1420614765900000000000000\) \([2]\) \(106168320\) \(4.1586\)  
145200.dj2 145200fs3 \([0, -1, 0, -572331008, 5258751040512]\) \(182864522286982801/463015182960\) \(52496616994547235840000000\) \([2]\) \(53084160\) \(3.8120\)  
145200.dj3 145200fs4 \([0, -1, 0, -518123008, -4520588991488]\) \(135670761487282321/643043610000\) \(72908222769613440000000000\) \([2, 2]\) \(53084160\) \(3.8120\)  
145200.dj4 145200fs5 \([0, -1, 0, -251923008, -9159922591488]\) \(-15595206456730321/310672490129100\) \(-35224017106278305606400000000\) \([2]\) \(106168320\) \(4.1586\)  
145200.dj5 145200fs2 \([0, -1, 0, -49611008, 12733120512]\) \(119102750067601/68309049600\) \(7744873485979238400000000\) \([2, 2]\) \(26542080\) \(3.4654\)  
145200.dj6 145200fs1 \([0, -1, 0, 12340992, 1581760512]\) \(1833318007919/1070530560\) \(-121376652121866240000000\) \([2]\) \(13271040\) \(3.1189\) \(\Gamma_0(N)\)-optimal