Properties

Label 36300n
Number of curves 2
Conductor 36300
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("36300.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 36300n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
36300.j2 36300n1 [0, -1, 0, 8067, 151362] [2] 92160 \(\Gamma_0(N)\)-optimal
36300.j1 36300n2 [0, -1, 0, -37308, 1331112] [2] 184320  

Rank

sage: E.rank()
 

The elliptic curves in class 36300n have rank \(1\).

Modular form 36300.2.a.j

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{7} + q^{9} - 2q^{13} + 4q^{17} + 6q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.