Properties

Label 14490.v
Number of curves $2$
Conductor $14490$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 14490.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.v1 14490t1 \([1, -1, 0, -12129, -166915]\) \(270701905514769/139540889600\) \(101725308518400\) \([2]\) \(49152\) \(1.3799\) \(\Gamma_0(N)\)-optimal
14490.v2 14490t2 \([1, -1, 0, 45471, -1330435]\) \(14262456319278831/9284810958080\) \(-6768627188440320\) \([2]\) \(98304\) \(1.7265\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14490.v have rank \(1\).

Complex multiplication

The elliptic curves in class 14490.v do not have complex multiplication.

Modular form 14490.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + 2 q^{11} + q^{14} + q^{16} - 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.