Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 79560.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79560.b1 79560bm4 \([0, 0, 0, -812163, 210014638]\) \(79364416584061444/20404090514925\) \(15231571953029452800\) \([2]\) \(1572864\) \(2.3902\)  
79560.b2 79560bm2 \([0, 0, 0, -285663, -56078462]\) \(13813960087661776/714574355625\) \(133356724544160000\) \([2, 2]\) \(786432\) \(2.0436\)  
79560.b3 79560bm1 \([0, 0, 0, -282018, -57645083]\) \(212670222886967296/616241925\) \(7187845813200\) \([2]\) \(393216\) \(1.6970\) \(\Gamma_0(N)\)-optimal
79560.b4 79560bm3 \([0, 0, 0, 182517, -221907818]\) \(900753985478876/29018422265625\) \(-21662136147600000000\) \([2]\) \(1572864\) \(2.3902\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 79560.2.a.b

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