Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("dw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.dw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.dw1 229320j2 \([0, 0, 0, -214347, 27960086]\) \(4253577358972/1142578125\) \(292554990000000000\) \([2]\) \(2457600\) \(2.0596\)  
229320.dw2 229320j1 \([0, 0, 0, -197967, 33899474]\) \(13404187799728/1584375\) \(101419063200000\) \([2]\) \(1228800\) \(1.7131\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 229320.dw have rank \(2\).

Complex multiplication

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

Modular form 229320.2.a.dw

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{13} - 4 q^{17} - 6 q^{19} + O(q^{20})\)  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.