Properties

Label 14994bg
Number of curves $4$
Conductor $14994$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14994bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14994.h4 14994bg1 \([1, -1, 0, 432, 933120]\) \(103823/4386816\) \(-376240191860736\) \([2]\) \(73728\) \(1.4757\) \(\Gamma_0(N)\)-optimal
14994.h3 14994bg2 \([1, -1, 0, -140688, 19984320]\) \(3590714269297/73410624\) \(6296144460669504\) \([2, 2]\) \(147456\) \(1.8222\)  
14994.h2 14994bg3 \([1, -1, 0, -299448, -33263784]\) \(34623662831857/14438442312\) \(1238329190382511752\) \([2]\) \(294912\) \(2.1688\)  
14994.h1 14994bg4 \([1, -1, 0, -2239848, 1290815784]\) \(14489843500598257/6246072\) \(535701366926712\) \([2]\) \(294912\) \(2.1688\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14994bg have rank \(0\).

Complex multiplication

The elliptic curves in class 14994bg do not have complex multiplication.

Modular form 14994.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2q^{5} - q^{8} + 2q^{10} + 6q^{13} + q^{16} + q^{17} + O(q^{20})\)  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 Cremona 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 Cremona labels.