Properties

Label 18720bj
Number of curves $4$
Conductor $18720$
CM no
Rank $0$
Graph

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

Elliptic curves in class 18720bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18720.bh3 18720bj1 \([0, 0, 0, -597, -5236]\) \(504358336/38025\) \(1774094400\) \([2, 2]\) \(6144\) \(0.51993\) \(\Gamma_0(N)\)-optimal
18720.bh1 18720bj2 \([0, 0, 0, -9372, -349216]\) \(30488290624/195\) \(582266880\) \([2]\) \(12288\) \(0.86651\)  
18720.bh2 18720bj3 \([0, 0, 0, -1947, 26894]\) \(2186875592/428415\) \(159905041920\) \([2]\) \(12288\) \(0.86651\)  
18720.bh4 18720bj4 \([0, 0, 0, 573, -23254]\) \(55742968/658125\) \(-245643840000\) \([2]\) \(12288\) \(0.86651\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18720bj have rank \(0\).

Complex multiplication

The elliptic curves in class 18720bj do not have complex multiplication.

Modular form 18720.2.a.bj

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.