Properties

Label 226512.ea
Number of curves $2$
Conductor $226512$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ea1")
 
E.isogeny_class()
 

Elliptic curves in class 226512.ea

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
226512.ea1 226512by2 \([0, 0, 0, -6308940, -6099338113]\) \(11107182592000/13\) \(32503665843792\) \([]\) \(3421440\) \(2.3066\)  
226512.ea2 226512by1 \([0, 0, 0, -79860, -7920781]\) \(22528000/2197\) \(5493119527600848\) \([]\) \(1140480\) \(1.7573\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 226512.ea have rank \(1\).

Complex multiplication

The elliptic curves in class 226512.ea do not have complex multiplication.

Modular form 226512.2.a.ea

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.