Properties

Label 47190i
Number of curves $2$
Conductor $47190$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.o2 47190i1 \([1, 1, 0, 163, -1239]\) \(356400829/760500\) \(-1012225500\) \([2]\) \(20736\) \(0.41222\) \(\Gamma_0(N)\)-optimal
47190.o1 47190i2 \([1, 1, 0, -1267, -14681]\) \(169204136291/32906250\) \(43798218750\) \([2]\) \(41472\) \(0.75880\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 47190.2.a.i

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