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Properties

Label 20510a
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 20510a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20510.b2 20510a1 \([1, 0, 1, -519009, 143872932]\) \(15461341616731869233929/8803814950000\) \(8803814950000\) \([3]\) \(112320\) \(1.8097\) \(\Gamma_0(N)\)-optimal
20510.b1 20510a2 \([1, 0, 1, -623024, 82090366]\) \(26744657491710624461689/12562375000000000000\) \(12562375000000000000\) \([]\) \(336960\) \(2.3591\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 20510.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} - 2 q^{9} + q^{10} + q^{12} - 4 q^{13} - q^{14} - q^{15} + q^{16} + 3 q^{17} + 2 q^{18} + 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.