Properties

Label 14490cb
Number of curves $2$
Conductor $14490$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14490cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.cb1 14490cb1 \([1, -1, 1, -212, -601]\) \(1439069689/579600\) \(422528400\) \([2]\) \(6144\) \(0.35311\) \(\Gamma_0(N)\)-optimal
14490.cb2 14490cb2 \([1, -1, 1, 688, -4921]\) \(49471280711/41992020\) \(-30612182580\) \([2]\) \(12288\) \(0.69968\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14490cb have rank \(0\).

Complex multiplication

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

Modular form 14490.2.a.cb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + 2q^{11} + 4q^{13} + q^{14} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.