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Properties

Label 154869k
Number of curves $2$
Conductor $154869$
CM no
Rank $0$
Graph

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

Elliptic curves in class 154869k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154869.r2 154869k1 \([1, 0, 1, 714, -9221]\) \(857375/1287\) \(-60548048847\) \([2]\) \(96768\) \(0.75428\) \(\Gamma_0(N)\)-optimal
154869.r1 154869k2 \([1, 0, 1, -4701, -93695]\) \(244140625/61347\) \(2886123661707\) \([2]\) \(193536\) \(1.1009\)  

Rank

sage: E.rank()
 

The elliptic curves in class 154869k have rank \(0\).

Complex multiplication

The elliptic curves in class 154869k do not have complex multiplication.

Modular form 154869.2.a.k

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