Properties

Label 14490ca
Number of curves $4$
Conductor $14490$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14490ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.by3 14490ca1 \([1, -1, 1, -1144112, -504199789]\) \(-227196402372228188089/19338934824115200\) \(-14098083486779980800\) \([2]\) \(368640\) \(2.4192\) \(\Gamma_0(N)\)-optimal
14490.by2 14490ca2 \([1, -1, 1, -18664592, -31031884141]\) \(986396822567235411402169/6336721794060000\) \(4619470187869740000\) \([2]\) \(737280\) \(2.7658\)  
14490.by4 14490ca3 \([1, -1, 1, 6782953, -20348881]\) \(47342661265381757089751/27397579603968000000\) \(-19972835531292672000000\) \([6]\) \(1105920\) \(2.9685\)  
14490.by1 14490ca4 \([1, -1, 1, -27131927, -142442449]\) \(3029968325354577848895529/1753440696000000000000\) \(1278258267384000000000000\) \([6]\) \(2211840\) \(3.3151\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14490.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} - 4q^{13} + q^{14} + q^{16} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.