Properties

Label 229320.du
Number of curves $2$
Conductor $229320$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("du1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.du

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.du1 229320cz2 \([0, 0, 0, -141267, -20140274]\) \(1775007362/29575\) \(5194819642521600\) \([2]\) \(1474560\) \(1.8140\)  
229320.du2 229320cz1 \([0, 0, 0, -17787, 431494]\) \(7086244/3185\) \(279721057674240\) \([2]\) \(737280\) \(1.4674\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 229320.du have rank \(1\).

Complex multiplication

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

Modular form 229320.2.a.du

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{13} - 8 q^{17} + 2 q^{19} + O(q^{20})\)  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.