Properties

Label 14784.e
Number of curves $4$
Conductor $14784$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 14784.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14784.e1 14784j3 \([0, -1, 0, -23969, 1428705]\) \(46477380430664/286446699\) \(9386285432832\) \([2]\) \(36864\) \(1.3275\)  
14784.e2 14784j2 \([0, -1, 0, -2409, -7191]\) \(377619516352/211789809\) \(867491057664\) \([2, 2]\) \(18432\) \(0.98092\)  
14784.e3 14784j1 \([0, -1, 0, -1804, -28850]\) \(10150654719808/19370043\) \(1239682752\) \([2]\) \(9216\) \(0.63434\) \(\Gamma_0(N)\)-optimal
14784.e4 14784j4 \([0, -1, 0, 9471, -66591]\) \(2866919053816/1712145897\) \(-56103596752896\) \([2]\) \(36864\) \(1.3275\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14784.e have rank \(0\).

Complex multiplication

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

Modular form 14784.2.a.e

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