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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 41070.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41070.k1 41070k2 \([1, 0, 1, -205379, -35410498]\) \(511189448451769/7077888000\) \(13265101651968000\) \([]\) \(598752\) \(1.8992\)  
41070.k2 41070k1 \([1, 0, 1, -20564, 1108946]\) \(513108539209/12597120\) \(23609031016320\) \([3]\) \(199584\) \(1.3499\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 41070.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.