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Properties

Label 190463.w
Number of curves $3$
Conductor $190463$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 190463.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190463.w1 190463w3 \([0, -1, 1, -122804408939, 16564189262475168]\) \(-360675992659311050823073792/56219378022244619\) \(-31925256147702285651467017379\) \([]\) \(564350976\) \(4.8737\)  
190463.w2 190463w2 \([0, -1, 1, -1321228029, 28776199131903]\) \(-449167881463536812032/369990050199923699\) \(-210105973069642713466400019659\) \([]\) \(188116992\) \(4.3244\)  
190463.w3 190463w1 \([0, -1, 1, 134240531, -641458502462]\) \(471114356703100928/585612268875179\) \(-332551201112180883119990339\) \([]\) \(62705664\) \(3.7751\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 190463.w have rank \(0\).

Complex multiplication

The elliptic curves in class 190463.w do not have complex multiplication.

Modular form 190463.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} + 3 q^{5} - 2 q^{9} + 3 q^{11} + 2 q^{12} - 3 q^{15} + 4 q^{16} + 6 q^{17} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.