Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 79560.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79560.bj1 79560bo4 \([0, 0, 0, -294267, 61440694]\) \(1887517194957938/21849165\) \(32620628551680\) \([2]\) \(393216\) \(1.7442\)  
79560.bj2 79560bo2 \([0, 0, 0, -18867, 907774]\) \(994958062276/98903025\) \(73830712550400\) \([2, 2]\) \(196608\) \(1.3976\)  
79560.bj3 79560bo1 \([0, 0, 0, -4287, -92414]\) \(46689225424/7249905\) \(1353006270720\) \([2]\) \(98304\) \(1.0510\) \(\Gamma_0(N)\)-optimal
79560.bj4 79560bo3 \([0, 0, 0, 23253, 4386886]\) \(931329171502/6107473125\) \(-9118408515840000\) \([2]\) \(393216\) \(1.7442\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 79560.2.a.bj

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4q^{11} - q^{13} - q^{17} + 8q^{19} + O(q^{20})\)  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.