Properties

Label 38720.h
Number of curves $2$
Conductor $38720$
CM no
Rank $0$
Graph

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

Elliptic curves in class 38720.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38720.h1 38720r2 \([0, 1, 0, -29201, -1925585]\) \(94875856/275\) \(7981945241600\) \([2]\) \(92160\) \(1.3464\)  
38720.h2 38720r1 \([0, 1, 0, -2581, -3621]\) \(1048576/605\) \(1097517470720\) \([2]\) \(46080\) \(0.99987\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38720.h have rank \(0\).

Complex multiplication

The elliptic curves in class 38720.h do not have complex multiplication.

Modular form 38720.2.a.h

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{9} + 2 q^{15} + 4 q^{17} - 4 q^{19} + O(q^{20})\) 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.