Properties

Label 36300k
Number of curves $4$
Conductor $36300$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 36300k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36300.y4 36300k1 \([0, -1, 0, 661467, 760600062]\) \(72268906496/606436875\) \(-268584979177968750000\) \([2]\) \(829440\) \(2.6013\) \(\Gamma_0(N)\)-optimal
36300.y3 36300k2 \([0, -1, 0, -9547908, 10459506312]\) \(13584145739344/1195803675\) \(8473756617146700000000\) \([2]\) \(1658880\) \(2.9479\)  
36300.y2 36300k3 \([0, -1, 0, -47254533, 125144546562]\) \(-26348629355659264/24169921875\) \(-10704622741699218750000\) \([2]\) \(2488320\) \(3.1506\)  
36300.y1 36300k4 \([0, -1, 0, -756238908, 8004796890312]\) \(6749703004355978704/5671875\) \(40192290187500000000\) \([2]\) \(4976640\) \(3.4972\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 36300k do not have complex multiplication.

Modular form 36300.2.a.k

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.