Properties

Label 47096.l
Number of curves $2$
Conductor $47096$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47096.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.l1 47096e2 \([0, -1, 0, -424144, 80724444]\) \(13854050788/3411821\) \(2078137034626601984\) \([2]\) \(806400\) \(2.2253\)  
47096.l2 47096e1 \([0, -1, 0, 63636, 7947668]\) \(187153328/288463\) \(-43925637029279488\) \([2]\) \(403200\) \(1.8787\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47096.l have rank \(0\).

Complex multiplication

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

Modular form 47096.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.