Properties

Label 36300.j
Number of curves $2$
Conductor $36300$
CM no
Rank $1$
Graph

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

Elliptic curves in class 36300.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36300.j1 36300n2 \([0, -1, 0, -37308, 1331112]\) \(810448/363\) \(2572306572000000\) \([2]\) \(184320\) \(1.6524\)  
36300.j2 36300n1 \([0, -1, 0, 8067, 151362]\) \(131072/99\) \(-43846134750000\) \([2]\) \(92160\) \(1.3058\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 36300.2.a.j

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