Properties

Label 6422.b
Number of curves $2$
Conductor $6422$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6422.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6422.b1 6422b2 \([1, 1, 0, -11833, -553405]\) \(-37966934881/4952198\) \(-23903313876182\) \([]\) \(23400\) \(1.3003\)  
6422.b2 6422b1 \([1, 1, 0, -3, 2605]\) \(-1/608\) \(-2934699872\) \([]\) \(4680\) \(0.49554\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6422.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 4 q^{5} + q^{6} - 3 q^{7} - q^{8} - 2 q^{9} - 4 q^{10} - 2 q^{11} - q^{12} + 3 q^{14} - 4 q^{15} + q^{16} + 3 q^{17} + 2 q^{18} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.