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Properties

Label 157146.j
Number of curves $2$
Conductor $157146$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 157146.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
157146.j1 157146b2 \([1, 0, 0, -38408316, -522985097928]\) \(-6266131592499446074204943809/114530114448469944018712104\) \(-114530114448469944018712104\) \([]\) \(48519408\) \(3.6813\)  
157146.j2 157146b1 \([1, 0, 0, -5245956, 4677234192]\) \(-15966056003238798715810369/212807477317047681024\) \(-212807477317047681024\) \([7]\) \(6931344\) \(2.7084\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 157146.j have rank \(1\).

Complex multiplication

The elliptic curves in class 157146.j do not have complex multiplication.

Modular form 157146.2.a.j

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