Properties

Label 1800.n
Number of curves $6$
Conductor $1800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1800.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1800.n1 1800r5 [0, 0, 0, -720075, 235187750] [2] 12288  
1800.n2 1800r3 [0, 0, 0, -45075, 3662750] [2, 2] 6144  
1800.n3 1800r6 [0, 0, 0, -18075, 8009750] [2] 12288  
1800.n4 1800r2 [0, 0, 0, -4575, -22750] [2, 2] 3072  
1800.n5 1800r1 [0, 0, 0, -3450, -77875] [2] 1536 \(\Gamma_0(N)\)-optimal
1800.n6 1800r4 [0, 0, 0, 17925, -180250] [2] 6144  

Rank

sage: E.rank()
 

The elliptic curves in class 1800.n have rank \(1\).

Complex multiplication

The elliptic curves in class 1800.n do not have complex multiplication.

Modular form 1800.2.a.n

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.