Properties

Label 46800.cj
Number of curves $3$
Conductor $46800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cj1")
 
E.isogeny_class()
 

Elliptic curves in class 46800.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.cj1 46800db3 \([0, 0, 0, -1654275, -818954750]\) \(-10730978619193/6656\) \(-310542336000000\) \([]\) \(466560\) \(2.1016\)  
46800.cj2 46800db2 \([0, 0, 0, -16275, -1592750]\) \(-10218313/17576\) \(-820025856000000\) \([]\) \(155520\) \(1.5523\)  
46800.cj3 46800db1 \([0, 0, 0, 1725, 45250]\) \(12167/26\) \(-1213056000000\) \([]\) \(51840\) \(1.0029\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46800.cj have rank \(1\).

Complex multiplication

The elliptic curves in class 46800.cj do not have complex multiplication.

Modular form 46800.2.a.cj

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.