Properties

Label 3450.y
Number of curves $2$
Conductor $3450$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3450.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.y1 3450x2 \([1, 0, 0, -788, 8442]\) \(3463512697/3174\) \(49593750\) \([2]\) \(2048\) \(0.40017\)  
3450.y2 3450x1 \([1, 0, 0, -38, 192]\) \(-389017/828\) \(-12937500\) \([2]\) \(1024\) \(0.053594\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3450.y have rank \(0\).

Complex multiplication

The elliptic curves in class 3450.y do not have complex multiplication.

Modular form 3450.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 2q^{7} + q^{8} + q^{9} - 6q^{11} + q^{12} + 2q^{13} + 2q^{14} + q^{16} + q^{18} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.