Properties

Label 70560cy
Number of curves $2$
Conductor $70560$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("cy1")
 
E.isogeny_class()
 

Elliptic curves in class 70560cy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70560.bm1 70560cy1 \([0, 0, 0, -11613, 474712]\) \(31554496/525\) \(2881741665600\) \([2]\) \(147456\) \(1.1893\) \(\Gamma_0(N)\)-optimal
70560.bm2 70560cy2 \([0, 0, 0, -588, 1339072]\) \(-64/2205\) \(-774612159713280\) \([2]\) \(294912\) \(1.5358\)  

Rank

sage: E.rank()
 

The elliptic curves in class 70560cy have rank \(2\).

Complex multiplication

The elliptic curves in class 70560cy do not have complex multiplication.

Modular form 70560.2.a.cy

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