Properties

Label 47040eb
Number of curves $2$
Conductor $47040$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eb1")
 
E.isogeny_class()
 

Elliptic curves in class 47040eb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47040.x1 47040eb1 \([0, -1, 0, -10061, 297165]\) \(2725888/675\) \(27892413158400\) \([2]\) \(86016\) \(1.2903\) \(\Gamma_0(N)\)-optimal
47040.x2 47040eb2 \([0, -1, 0, 24239, 1854385]\) \(2382032/3645\) \(-2409904496885760\) \([2]\) \(172032\) \(1.6369\)  

Rank

sage: E.rank()
 

The elliptic curves in class 47040eb have rank \(1\).

Complex multiplication

The elliptic curves in class 47040eb do not have complex multiplication.

Modular form 47040.2.a.eb

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