Properties

Label 6468.b
Number of curves 2
Conductor 6468
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6468.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6468.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6468.b1 6468h2 [0, -1, 0, -604, 2920] [2] 4320  
6468.b2 6468h1 [0, -1, 0, 131, 274] [2] 2160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6468.b have rank \(0\).

Modular form 6468.2.a.b

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

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.