Properties

Label 229320.ed
Number of curves $2$
Conductor $229320$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ed1")
 
E.isogeny_class()
 

Elliptic curves in class 229320.ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.ed1 229320dg1 \([0, 0, 0, -4560087, -1464657334]\) \(477625344356176/234195040625\) \(5142016049111978400000\) \([2]\) \(14745600\) \(2.8593\) \(\Gamma_0(N)\)-optimal
229320.ed2 229320dg2 \([0, 0, 0, 16616733, -11218700626]\) \(5777565954713276/3962587890625\) \(-348012331520490000000000\) \([2]\) \(29491200\) \(3.2058\)  

Rank

sage: E.rank()
 

The elliptic curves in class 229320.ed have rank \(0\).

Complex multiplication

The elliptic curves in class 229320.ed do not have complex multiplication.

Modular form 229320.2.a.ed

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{11} - q^{13} - 6 q^{17} - 6 q^{19} + O(q^{20})\) 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 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.