Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("dv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320dv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.ba1 229320dv1 \([0, 0, 0, -5963643, 5605479558]\) \(267080942160036/1990625\) \(174825661046400000\) \([2]\) \(6881280\) \(2.4845\) \(\Gamma_0(N)\)-optimal
229320.ba2 229320dv2 \([0, 0, 0, -5840163, 5848710462]\) \(-125415986034978/11552734375\) \(-2029226422860000000000\) \([2]\) \(13762560\) \(2.8311\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 229320.2.a.dv

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2q^{11} - q^{13} - 8q^{19} + O(q^{20})\)  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.