Properties

Label 47190.n
Number of curves $6$
Conductor $47190$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.n1 47190k6 \([1, 1, 0, -1090817, 438052179]\) \(81025909800741361/11088090\) \(19643227808490\) \([2]\) \(655360\) \(1.9630\)  
47190.n2 47190k4 \([1, 1, 0, -102247, -12616919]\) \(66730743078481/60937500\) \(107954498437500\) \([2]\) \(327680\) \(1.6164\)  
47190.n3 47190k3 \([1, 1, 0, -68367, 6782769]\) \(19948814692561/231344100\) \(409840185140100\) \([2, 2]\) \(327680\) \(1.6164\)  
47190.n4 47190k5 \([1, 1, 0, -13917, 17356959]\) \(-168288035761/73415764890\) \(-130060505864293290\) \([2]\) \(655360\) \(1.9630\)  
47190.n5 47190k2 \([1, 1, 0, -7867, -102131]\) \(30400540561/15210000\) \(26945442810000\) \([2, 2]\) \(163840\) \(1.2699\)  
47190.n6 47190k1 \([1, 1, 0, 1813, -11139]\) \(371694959/249600\) \(-442181625600\) \([2]\) \(81920\) \(0.92330\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47190.n have rank \(1\).

Complex multiplication

The elliptic curves in class 47190.n do not have complex multiplication.

Modular form 47190.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - q^{15} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.