Properties

Label 14994t
Number of curves 4
Conductor 14994
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14994.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14994t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14994.u4 14994t1 [1, -1, 0, -1332, 11920] [2] 13824 \(\Gamma_0(N)\)-optimal
14994.u3 14994t2 [1, -1, 0, -18972, 1010344] [2] 27648  
14994.u2 14994t3 [1, -1, 0, -45432, -3715412] [2] 41472  
14994.u1 14994t4 [1, -1, 0, -49842, -2947190] [2] 82944  

Rank

sage: E.rank()
 

The elliptic curves in class 14994t have rank \(1\).

Modular form 14994.2.a.u

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} - 6q^{11} - 2q^{13} + q^{16} - q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.