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Properties

Label 102966.k
Number of curves $2$
Conductor $102966$
CM no
Rank $1$
Graph

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

Elliptic curves in class 102966.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102966.k1 102966i2 \([1, 0, 1, -3896319603, 93611210984980]\) \(1294373635812597347281/2083292441154\) \(10528779051729452304140274\) \([]\) \(72072000\) \(4.0657\)  
102966.k2 102966i1 \([1, 0, 1, -36639093, -81138720800]\) \(1076291879750641/60150618144\) \(303995999674588808434464\) \([]\) \(14414400\) \(3.2610\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 102966.k have rank \(1\).

Complex multiplication

The elliptic curves in class 102966.k do not have complex multiplication.

Modular form 102966.2.a.k

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.