Properties

Label 42350bo
Number of curves $2$
Conductor $42350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 42350bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42350.f1 42350bo1 \([1, 0, 1, -134676, -67505902]\) \(-243979633825/1636214272\) \(-1811658369949120000\) \([]\) \(622080\) \(2.1868\) \(\Gamma_0(N)\)-optimal
42350.f2 42350bo2 \([1, 0, 1, 1196324, 1693673298]\) \(171015136702175/1218033273688\) \(-1348637652729991855000\) \([]\) \(1866240\) \(2.7361\)  

Rank

sage: E.rank()
 

The elliptic curves in class 42350bo have rank \(1\).

Complex multiplication

The elliptic curves in class 42350bo do not have complex multiplication.

Modular form 42350.2.a.bo

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{12} + q^{13} + q^{14} + q^{16} - q^{18} + q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.