Properties

Label 8624.y
Number of curves $2$
Conductor $8624$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8624.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8624.y1 8624t2 \([0, -1, 0, -44704, 1440384]\) \(59776471/29282\) \(4839974175432704\) \([2]\) \(43008\) \(1.7029\)  
8624.y2 8624t1 \([0, -1, 0, 10176, 167168]\) \(704969/484\) \(-79999573147648\) \([2]\) \(21504\) \(1.3564\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8624.y have rank \(1\).

Complex multiplication

The elliptic curves in class 8624.y do not have complex multiplication.

Modular form 8624.2.a.y

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 2 q^{5} + q^{9} - q^{11} + 2 q^{13} - 4 q^{15} + 2 q^{19} + O(q^{20})\) 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.