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Properties

Label 20510.a
Number of curves $2$
Conductor $20510$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 20510.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20510.a1 20510b2 \([1, -1, 0, -3689, -85305]\) \(5552849431422441/1472310350\) \(1472310350\) \([2]\) \(13824\) \(0.74337\)  
20510.a2 20510b1 \([1, -1, 0, -259, -927]\) \(1925599082121/689423140\) \(689423140\) \([2]\) \(6912\) \(0.39680\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20510.a have rank \(1\).

Complex multiplication

The elliptic curves in class 20510.a do not have complex multiplication.

Modular form 20510.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - 3 q^{9} - q^{10} - 2 q^{13} + q^{14} + q^{16} + 4 q^{17} + 3 q^{18} - 6 q^{19} + O(q^{20})\) 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.