Properties

Label 47096c
Number of curves $2$
Conductor $47096$
CM no
Rank $1$
Graph

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

Elliptic curves in class 47096c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.d1 47096c1 \([0, 1, 0, -6167, -60770]\) \(2725888/1421\) \(13523903026256\) \([2]\) \(94080\) \(1.2115\) \(\Gamma_0(N)\)-optimal
47096.d2 47096c2 \([0, 1, 0, 23268, -449312]\) \(9148592/5887\) \(-896441572026112\) \([2]\) \(188160\) \(1.5581\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 47096.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + 2q^{5} - q^{7} + q^{9} + 6q^{13} - 4q^{15} - 4q^{17} - 2q^{19} + O(q^{20})\)  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.