Properties

Label 12882.e
Number of curves $2$
Conductor $12882$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12882.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12882.e1 12882e1 \([1, 1, 0, -494883, -79253235]\) \(13403946614821979039929/5057590268826067968\) \(5057590268826067968\) \([2]\) \(632320\) \(2.2885\) \(\Gamma_0(N)\)-optimal
12882.e2 12882e2 \([1, 1, 0, 1548157, -563453715]\) \(410363075617640914325831/374944243169850027552\) \(-374944243169850027552\) \([2]\) \(1264640\) \(2.6351\)  

Rank

sage: E.rank()
 

The elliptic curves in class 12882.e have rank \(1\).

Complex multiplication

The elliptic curves in class 12882.e do not have complex multiplication.

Modular form 12882.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 4q^{5} + q^{6} - 4q^{7} - q^{8} + q^{9} - 4q^{10} - q^{12} + 4q^{14} - 4q^{15} + q^{16} - 6q^{17} - q^{18} + q^{19} + O(q^{20})\)  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.