Properties

Label 1792.h
Number of curves $2$
Conductor $1792$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1792.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1792.h1 1792d2 \([0, -1, 0, -141, 533]\) \(9528128/2401\) \(78675968\) \([2]\) \(768\) \(0.22494\)  
1792.h2 1792d1 \([0, -1, 0, -131, 623]\) \(489303872/49\) \(25088\) \([2]\) \(384\) \(-0.12163\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1792.h have rank \(0\).

Complex multiplication

The elliptic curves in class 1792.h do not have complex multiplication.

Modular form 1792.2.a.h

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + 4 q^{5} + q^{7} + q^{9} + 2 q^{11} - 4 q^{13} + 8 q^{15} + 2 q^{17} - 6 q^{19} + O(q^{20})\)  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.