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Properties

Label 369600.bh
Number of curves $6$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bh1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 369600.bh have rank \(0\).

L-function data

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

Complex multiplication

The elliptic curves in class 369600.bh do not have complex multiplication.

Modular form 369600.2.a.bh

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 369600.bh

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.bh1 369600bh5 \([0, -1, 0, -4726433, 3952828737]\) \(5701568801608514/6277868289\) \(12857074255872000000\) \([2]\) \(12582912\) \(2.5816\)  
369600.bh2 369600bh3 \([0, -1, 0, -370433, 28072737]\) \(5489767279588/2847396321\) \(2915733832704000000\) \([2, 2]\) \(6291456\) \(2.2350\)  
369600.bh3 369600bh2 \([0, -1, 0, -208433, -36241263]\) \(3911877700432/38900169\) \(9958443264000000\) \([2, 2]\) \(3145728\) \(1.8885\)  
369600.bh4 369600bh1 \([0, -1, 0, -207933, -36425763]\) \(62140690757632/6237\) \(99792000000\) \([2]\) \(1572864\) \(1.5419\) \(\Gamma_0(N)\)-optimal
369600.bh5 369600bh4 \([0, -1, 0, -54433, -88755263]\) \(-17418812548/3314597517\) \(-3394147857408000000\) \([2]\) \(6291456\) \(2.2350\)  
369600.bh6 369600bh6 \([0, -1, 0, 1393567, 216820737]\) \(146142660369886/94532266521\) \(-193602081835008000000\) \([2]\) \(12582912\) \(2.5816\)