Properties

Label 20230.r
Number of curves $2$
Conductor $20230$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 20230.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20230.r1 20230n1 \([1, 1, 1, -3082191, 2079399509]\) \(27306250652897/31360000\) \(3718915806945920000\) \([2]\) \(783360\) \(2.4762\) \(\Gamma_0(N)\)-optimal
20230.r2 20230n2 \([1, 1, 1, -2296111, 3166390933]\) \(-11289171456737/30012500000\) \(-3559118643366212500000\) \([2]\) \(1566720\) \(2.8228\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20230.r have rank \(1\).

Complex multiplication

The elliptic curves in class 20230.r do not have complex multiplication.

Modular form 20230.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} - q^{5} + 2 q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2 q^{11} + 2 q^{12} - 2 q^{13} + q^{14} - 2 q^{15} + q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) 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.