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Properties

Label 816.h
Number of curves $2$
Conductor $816$
CM no
Rank $1$
Graph

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

Elliptic curves in class 816.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
816.h1 816j1 \([0, 1, 0, -40, -76]\) \(1771561/612\) \(2506752\) \([2]\) \(192\) \(-0.070381\) \(\Gamma_0(N)\)-optimal
816.h2 816j2 \([0, 1, 0, 120, -396]\) \(46268279/46818\) \(-191766528\) \([2]\) \(384\) \(0.27619\)  

Rank

sage: E.rank()
 

The elliptic curves in class 816.h have rank \(1\).

Complex multiplication

The elliptic curves in class 816.h do not have complex multiplication.

Modular form 816.2.a.h

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