Properties

Label 14994z
Number of curves $3$
Conductor $14994$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 14994z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14994.b3 14994z1 \([1, -1, 0, 47619, 107925061]\) \(139233463487/58763045376\) \(-5039878460046506496\) \([]\) \(414720\) \(2.2678\) \(\Gamma_0(N)\)-optimal
14994.b2 14994z2 \([1, -1, 0, -428661, -2917691267]\) \(-101566487155393/42823570577256\) \(-3672811535780977943976\) \([]\) \(1244160\) \(2.8171\)  
14994.b1 14994z3 \([1, -1, 0, -168330591, -840593126129]\) \(-6150311179917589675873/244053849830826\) \(-20931552015106452245946\) \([]\) \(3732480\) \(3.3664\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14994.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} - q^{8} + 3 q^{10} - 3 q^{11} - 5 q^{13} + q^{16} - q^{17} - 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.