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Properties

Label 119952.bh
Number of curves $6$
Conductor $119952$
CM no
Rank $1$
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 119952.bh have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(7\)\(1\)
\(17\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 2 T + 5 T^{2}\) 1.5.c
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 119952.bh do not have complex multiplication.

Modular form 119952.2.a.bh

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{5} - 4 q^{11} + 2 q^{13} + q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 119952.bh

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bh1 119952gt6 \([0, 0, 0, -195761811, 1054241418706]\) \(2361739090258884097/5202\) \(1827452360466432\) \([2]\) \(9437184\) \(3.0625\)  
119952.bh2 119952gt4 \([0, 0, 0, -12235251, 16472132530]\) \(576615941610337/27060804\) \(9506407179146379264\) \([2, 2]\) \(4718592\) \(2.7159\)  
119952.bh3 119952gt5 \([0, 0, 0, -11600211, 18258246034]\) \(-491411892194497/125563633938\) \(-44110257444971374583808\) \([2]\) \(9437184\) \(3.0625\)  
119952.bh4 119952gt2 \([0, 0, 0, -804531, 229079410]\) \(163936758817/30338064\) \(10657702166240231424\) \([2, 2]\) \(2359296\) \(2.3693\)  
119952.bh5 119952gt1 \([0, 0, 0, -240051, -41983886]\) \(4354703137/352512\) \(123836771721019392\) \([2]\) \(1179648\) \(2.0228\) \(\Gamma_0(N)\)-optimal
119952.bh6 119952gt3 \([0, 0, 0, 1594509, 1334077234]\) \(1276229915423/2927177028\) \(-1028311528127972917248\) \([2]\) \(4718592\) \(2.7159\)