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Properties

Label 320790.h
Number of curves $2$
Conductor $320790$
CM no
Rank $0$
Graph

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

Elliptic curves in class 320790.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320790.h1 320790h2 \([1, 1, 0, -14949542, -21533211756]\) \(3115782459247193/114969715200\) \(13634014387032863654400\) \([2]\) \(40108032\) \(3.0165\)  
320790.h2 320790h1 \([1, 1, 0, -2372262, 947418516]\) \(12450066246233/3928227840\) \(465840197941997076480\) \([2]\) \(20054016\) \(2.6699\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 320790.h have rank \(0\).

Complex multiplication

The elliptic curves in class 320790.h do not have complex multiplication.

Modular form 320790.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{10} - q^{12} + 2 q^{13} + 4 q^{14} - q^{15} + q^{16} - q^{18} + 2 q^{19} + O(q^{20})\) 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.