Properties

Label 9360.b
Number of curves $4$
Conductor $9360$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9360.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9360.b1 9360o4 \([0, 0, 0, -74883, 7887202]\) \(31103978031362/195\) \(291133440\) \([2]\) \(24576\) \(1.2297\)  
9360.b2 9360o3 \([0, 0, 0, -6483, 19762]\) \(20183398562/11567205\) \(17269744527360\) \([2]\) \(24576\) \(1.2297\)  
9360.b3 9360o2 \([0, 0, 0, -4683, 123082]\) \(15214885924/38025\) \(28385510400\) \([2, 2]\) \(12288\) \(0.88311\)  
9360.b4 9360o1 \([0, 0, 0, -183, 3382]\) \(-3631696/24375\) \(-4548960000\) \([2]\) \(6144\) \(0.53654\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9360.b have rank \(1\).

Complex multiplication

The elliptic curves in class 9360.b do not have complex multiplication.

Modular form 9360.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4q^{7} + 4q^{11} + q^{13} - 6q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.