Properties

Label 1800.v
Number of curves 4
Conductor 1800
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1800.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1800.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1800.v1 1800g3 [0, 0, 0, -24075, 1437750] [2] 3072  
1800.v2 1800g2 [0, 0, 0, -1575, 20250] [2, 2] 1536  
1800.v3 1800g1 [0, 0, 0, -450, -3375] [2] 768 \(\Gamma_0(N)\)-optimal
1800.v4 1800g4 [0, 0, 0, 2925, 114750] [2] 3072  

Rank

sage: E.rank()
 

The elliptic curves in class 1800.v have rank \(0\).

Modular form 1800.2.a.v

sage: E.q_eigenform(10)
 
\( q + 4q^{7} - 4q^{11} + 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.