Properties

Label 6422.h
Number of curves $3$
Conductor $6422$
CM no
Rank $0$
Graph

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

Elliptic curves in class 6422.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6422.h1 6422f3 \([1, 0, 0, -14453, -5380831]\) \(-69173457625/2550136832\) \(-12309023411929088\) \([]\) \(36936\) \(1.7676\)  
6422.h2 6422f1 \([1, 0, 0, -2623, 51505]\) \(-413493625/152\) \(-733674968\) \([]\) \(4104\) \(0.66903\) \(\Gamma_0(N)\)-optimal
6422.h3 6422f2 \([1, 0, 0, 1602, 196676]\) \(94196375/3511808\) \(-16950826460672\) \([]\) \(12312\) \(1.2183\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6422.h have rank \(0\).

Complex multiplication

The elliptic curves in class 6422.h do not have complex multiplication.

Modular form 6422.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2q^{9} + 6q^{11} + q^{12} + q^{14} + q^{16} + 3q^{17} - 2q^{18} - q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.