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Properties

Label 156090h
Number of curves $2$
Conductor $156090$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 156090h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
156090.bx2 156090h1 \([1, 0, 0, -4540, -79408]\) \(5841725401/1857600\) \(3290851713600\) \([2]\) \(403200\) \(1.1057\) \(\Gamma_0(N)\)-optimal
156090.bx1 156090h2 \([1, 0, 0, -28740, 1813032]\) \(1481933914201/53916840\) \(95516970987240\) \([2]\) \(806400\) \(1.4523\)  

Rank

sage: E.rank()
 

The elliptic curves in class 156090h have rank \(0\).

Complex multiplication

The elliptic curves in class 156090h do not have complex multiplication.

Modular form 156090.2.a.h

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