Properties

Label 47096.i
Number of curves $4$
Conductor $47096$
CM no
Rank $1$
Graph

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

Elliptic curves in class 47096.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.i1 47096a4 \([0, 0, 0, -251459, 48534110]\) \(1443468546/7\) \(8527387129856\) \([2]\) \(193536\) \(1.6816\)  
47096.i2 47096a3 \([0, 0, 0, -49619, -3365682]\) \(11090466/2401\) \(2924893785540608\) \([2]\) \(193536\) \(1.6816\)  
47096.i3 47096a2 \([0, 0, 0, -15979, 731670]\) \(740772/49\) \(29845854954496\) \([2, 2]\) \(96768\) \(1.3350\)  
47096.i4 47096a1 \([0, 0, 0, 841, 48778]\) \(432/7\) \(-1065923391232\) \([2]\) \(48384\) \(0.98847\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47096.i have rank \(1\).

Complex multiplication

The elliptic curves in class 47096.i do not have complex multiplication.

Modular form 47096.2.a.i

sage: E.q_eigenform(10)
 
\(q + 2q^{5} - q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.