Properties

Label 119952.bh
Number of curves $6$
Conductor $119952$
CM no
Rank $1$
Graph

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

Elliptic curves in class 119952.bh

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 \([0, 0, 0, 1594509, 1334077234]\) \(1276229915423/2927177028\) \(-1028311528127972917248\) \([2]\) \(4718592\) \(2.7159\)  

Rank

sage: E.rank()
 

The elliptic curves in class 119952.bh have rank \(1\).

Complex multiplication

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

Modular form 119952.2.a.bh

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

Isogeny matrix

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

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

The vertices are labelled with LMFDB labels.