Properties

Label 14784.f
Number of curves $4$
Conductor $14784$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14784.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14784.f1 14784bv3 \([0, -1, 0, -2560929, 1119339585]\) \(14171198121996897746/4077720290568771\) \(534474953925429952512\) \([2]\) \(737280\) \(2.6837\)  
14784.f2 14784bv2 \([0, -1, 0, -2347969, 1385411809]\) \(21843440425782779332/3100814593569\) \(203214985204137984\) \([2, 2]\) \(368640\) \(2.3371\)  
14784.f3 14784bv1 \([0, -1, 0, -2347889, 1385510865]\) \(87364831012240243408/1760913\) \(28850798592\) \([2]\) \(184320\) \(1.9906\) \(\Gamma_0(N)\)-optimal
14784.f4 14784bv4 \([0, -1, 0, -2136289, 1645143169]\) \(-8226100326647904626/4152140742401883\) \(-544229391388099608576\) \([4]\) \(737280\) \(2.6837\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14784.f have rank \(1\).

Complex multiplication

The elliptic curves in class 14784.f do not have complex multiplication.

Modular form 14784.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{5} - q^{7} + q^{9} + q^{11} + 6q^{13} + 2q^{15} - 2q^{17} - 8q^{19} + O(q^{20})\)  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.