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Properties

Label 101478.k
Number of curves $2$
Conductor $101478$
CM no
Rank $0$
Graph

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

Elliptic curves in class 101478.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101478.k1 101478k2 \([1, 0, 0, -3334962226, -74128716508108]\) \(-4102007684809181687432274264918049/3936639679171948631439024\) \(-3936639679171948631439024\) \([]\) \(69895168\) \(4.0142\)  
101478.k2 101478k1 \([1, 0, 0, 8938334, 2268820292]\) \(78975693098270145722349791/47925805879636550221824\) \(-47925805879636550221824\) \([7]\) \(9985024\) \(3.0412\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 101478.k have rank \(0\).

Complex multiplication

The elliptic curves in class 101478.k do not have complex multiplication.

Modular form 101478.2.a.k

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.