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("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1800.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1800.v1 1800g3 \([0, 0, 0, -24075, 1437750]\) \(132304644/5\) \(58320000000\) \([2]\) \(3072\) \(1.1518\)  
1800.v2 1800g2 \([0, 0, 0, -1575, 20250]\) \(148176/25\) \(72900000000\) \([2, 2]\) \(1536\) \(0.80524\)  
1800.v3 1800g1 \([0, 0, 0, -450, -3375]\) \(55296/5\) \(911250000\) \([2]\) \(768\) \(0.45866\) \(\Gamma_0(N)\)-optimal
1800.v4 1800g4 \([0, 0, 0, 2925, 114750]\) \(237276/625\) \(-7290000000000\) \([2]\) \(3072\) \(1.1518\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1800.2.a.v

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.