Properties

Label 79560.u
Number of curves $4$
Conductor $79560$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 79560.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79560.u1 79560bk4 \([0, 0, 0, -2291403, 1335058598]\) \(891190736491222802/3729375\) \(5567927040000\) \([2]\) \(983040\) \(2.0772\)  
79560.u2 79560bk2 \([0, 0, 0, -143283, 20838782]\) \(435792975088324/890127225\) \(664476412953600\) \([2, 2]\) \(491520\) \(1.7306\)  
79560.u3 79560bk3 \([0, 0, 0, -94683, 35195222]\) \(-62875617222962/322034842935\) \(-480795444223211520\) \([2]\) \(983040\) \(2.0772\)  
79560.u4 79560bk1 \([0, 0, 0, -12063, 79778]\) \(1040212820176/587242305\) \(109593507928320\) \([2]\) \(245760\) \(1.3840\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 79560.2.a.u

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