Properties

Label 79560w
Number of curves $2$
Conductor $79560$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 79560w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79560.bm1 79560w1 \([0, 0, 0, -2529147, -1545816314]\) \(2396726313900986596/4154072495625\) \(3100998501694080000\) \([2]\) \(1474560\) \(2.4421\) \(\Gamma_0(N)\)-optimal
79560.bm2 79560w2 \([0, 0, 0, -1738227, -2530195346]\) \(-389032340685029858/1627263833203125\) \(-2429491884861600000000\) \([2]\) \(2949120\) \(2.7886\)  

Rank

sage: E.rank()
 

The elliptic curves in class 79560w have rank \(0\).

Complex multiplication

The elliptic curves in class 79560w do not have complex multiplication.

Modular form 79560.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{5} - 2 q^{11} - q^{13} + q^{17} - 8 q^{19} + O(q^{20})\) 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.