Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("dp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320dp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.a1 229320dp1 \([0, 0, 0, -765723, -257800858]\) \(565357377316/257985\) \(22657405671613440\) \([2]\) \(3538944\) \(2.0955\) \(\Gamma_0(N)\)-optimal
229320.a2 229320dp2 \([0, 0, 0, -642243, -343718242]\) \(-166792350818/194041575\) \(-34083211674584217600\) \([2]\) \(7077888\) \(2.4421\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 229320.2.a.dp

sage: E.q_eigenform(10)
 
\(q - q^{5} - 6q^{11} - q^{13} - 4q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.