Properties

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

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 14490.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.bc1 14490w1 \([1, -1, 0, -1010574, -390768620]\) \(156567200830221067489/16905000000\) \(12323745000000\) \([2]\) \(139776\) \(1.9387\) \(\Gamma_0(N)\)-optimal
14490.bc2 14490w2 \([1, -1, 0, -1008054, -392816372]\) \(-155398856216042825569/1627294921875000\) \(-1186297998046875000\) \([2]\) \(279552\) \(2.2853\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14490.2.a.bc

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