Properties

Label 14994.u
Number of curves $4$
Conductor $14994$
CM no
Rank $1$
Graph

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

Elliptic curves in class 14994.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14994.u1 14994t4 \([1, -1, 0, -49842, -2947190]\) \(159661140625/48275138\) \(4140371326999698\) \([2]\) \(82944\) \(1.7017\)  
14994.u2 14994t3 \([1, -1, 0, -45432, -3715412]\) \(120920208625/19652\) \(1685475809892\) \([2]\) \(41472\) \(1.3552\)  
14994.u3 14994t2 \([1, -1, 0, -18972, 1010344]\) \(8805624625/2312\) \(198291271752\) \([2]\) \(27648\) \(1.1524\)  
14994.u4 14994t1 \([1, -1, 0, -1332, 11920]\) \(3048625/1088\) \(93313539648\) \([2]\) \(13824\) \(0.80587\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14994.2.a.u

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.