Properties

Label 14490.c
Number of curves $4$
Conductor $14490$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 14490.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.c1 14490f3 \([1, -1, 0, -1622880, -795346394]\) \(648418741232906810881/33810\) \(24647490\) \([2]\) \(98304\) \(1.8117\)  
14490.c2 14490f4 \([1, -1, 0, -103500, -11873750]\) \(168197522113656001/13424780328750\) \(9786664859658750\) \([2]\) \(98304\) \(1.8117\)  
14490.c3 14490f2 \([1, -1, 0, -101430, -12408224]\) \(158306179791523681/1143116100\) \(833331636900\) \([2, 2]\) \(49152\) \(1.4651\)  
14490.c4 14490f1 \([1, -1, 0, -6210, -201020]\) \(-36333758230561/3290930160\) \(-2399088086640\) \([2]\) \(24576\) \(1.1186\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14490.2.a.c

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.