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Properties

Label 41070.q
Number of curves $2$
Conductor $41070$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 41070.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41070.q1 41070r1 \([1, 0, 1, -18973, 56888]\) \(14910549714397/8599633920\) \(435597256949760\) \([2]\) \(186624\) \(1.4985\) \(\Gamma_0(N)\)-optimal
41070.q2 41070r2 \([1, 0, 1, 75747, 473656]\) \(948905782000163/550998028800\) \(-27909703152806400\) \([2]\) \(373248\) \(1.8451\)  

Rank

sage: E.rank()
 

The elliptic curves in class 41070.q have rank \(0\).

Complex multiplication

The elliptic curves in class 41070.q do not have complex multiplication.

Modular form 41070.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 2 q^{7} - q^{8} + q^{9} - q^{10} + 4 q^{11} + q^{12} + 2 q^{13} - 2 q^{14} + q^{15} + q^{16} - 2 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.