Properties

Label 129285.h
Number of curves $2$
Conductor $129285$
CM no
Rank $0$
Graph

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

Elliptic curves in class 129285.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129285.h1 129285be1 \([1, -1, 1, -30452, 1866206]\) \(887503681/89505\) \(314945160328305\) \([2]\) \(430080\) \(1.5180\) \(\Gamma_0(N)\)-optimal
129285.h2 129285be2 \([1, -1, 1, 37993, 9011864]\) \(1723683599/10989225\) \(-38668266906975225\) \([2]\) \(860160\) \(1.8646\)  

Rank

sage: E.rank()
 

The elliptic curves in class 129285.h have rank \(0\).

Complex multiplication

The elliptic curves in class 129285.h do not have complex multiplication.

Modular form 129285.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.