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Properties

Label 14490.bi
Number of curves $2$
Conductor $14490$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 14490.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.bi1 14490bg2 \([1, -1, 1, -35837993, -14451870743]\) \(258620799050621485981803/145075171220000000000\) \(2855514595123260000000000\) \([2]\) \(2534400\) \(3.3828\)  
14490.bi2 14490bg1 \([1, -1, 1, -22290473, 40296367081]\) \(62228632040416581492843/382900201062400000\) \(7536624657511219200000\) \([2]\) \(1267200\) \(3.0362\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14490.2.a.bi

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