Properties

Label 169050bh
Number of curves $4$
Conductor $169050$
CM no
Rank $0$
Graph

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

Elliptic curves in class 169050bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.hx3 169050bh1 \([1, 0, 0, -155726313, -801117769383]\) \(-227196402372228188089/19338934824115200\) \(-35550099111286393200000000\) \([2]\) \(53084160\) \(3.6476\) \(\Gamma_0(N)\)-optimal
169050.hx2 169050bh2 \([1, 0, 0, -2540458313, -49285104061383]\) \(986396822567235411402169/6336721794060000\) \(11648577849208827187500000\) \([2]\) \(106168320\) \(3.9942\)  
169050.hx4 169050bh3 \([1, 0, 0, 923235312, -29543563008]\) \(47342661265381757089751/27397579603968000000\) \(-50364028794175488000000000000\) \([2]\) \(159252480\) \(4.1969\)  
169050.hx1 169050bh4 \([1, 0, 0, -3692956688, -237272203008]\) \(3029968325354577848895529/1753440696000000000000\) \(3223289756932875000000000000000\) \([2]\) \(318504960\) \(4.5435\)  

Rank

sage: E.rank()
 

The elliptic curves in class 169050bh have rank \(0\).

Complex multiplication

The elliptic curves in class 169050bh do not have complex multiplication.

Modular form 169050.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{12} - 4q^{13} + q^{16} + q^{18} - 2q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.