Properties

Label 129360.hn
Number of curves $2$
Conductor $129360$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("hn1")
 
E.isogeny_class()
 

Elliptic curves in class 129360.hn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129360.hn1 129360hv1 \([0, 1, 0, -132120, -15623532]\) \(529278808969/88704000\) \(42745597526016000\) \([2]\) \(1105920\) \(1.9122\) \(\Gamma_0(N)\)-optimal
129360.hn2 129360hv2 \([0, 1, 0, 244200, -88027500]\) \(3342032927351/8893500000\) \(-4285691418624000000\) \([2]\) \(2211840\) \(2.2588\)  

Rank

sage: E.rank()
 

The elliptic curves in class 129360.hn have rank \(0\).

Complex multiplication

The elliptic curves in class 129360.hn do not have complex multiplication.

Modular form 129360.2.a.hn

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + q^{11} + q^{15} - 4 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.