Properties

Label 9576.e
Number of curves $4$
Conductor $9576$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9576.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9576.e1 9576g3 \([0, 0, 0, -29091, 1584830]\) \(1823652903746/328593657\) \(490587701151744\) \([2]\) \(40960\) \(1.5379\)  
9576.e2 9576g2 \([0, 0, 0, -8571, -282490]\) \(93280467172/7800849\) \(5823302575104\) \([2, 2]\) \(20480\) \(1.1913\)  
9576.e3 9576g1 \([0, 0, 0, -8391, -295846]\) \(350104249168/2793\) \(521240832\) \([2]\) \(10240\) \(0.84476\) \(\Gamma_0(N)\)-optimal
9576.e4 9576g4 \([0, 0, 0, 9069, -1295026]\) \(55251546334/517244049\) \(-772241227204608\) \([2]\) \(40960\) \(1.5379\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9576.e have rank \(0\).

Complex multiplication

The elliptic curves in class 9576.e do not have complex multiplication.

Modular form 9576.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - q^{7} + 4 q^{11} - 6 q^{13} - 2 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.