Elliptic curve isogeny class 28.2-a over number field \(\Q(\sqrt{205}) \)

• Base field: \(\Q(\sqrt{205}) \)
• Label: 2.2.205.1-28.2-a
• Conductor: 28.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{205}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 51 \); class number \(2\).

Elliptic curves in class 28.2-a over \(\Q(\sqrt{205}) \)

Isogeny class 28.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
28.2-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -2724 a - 18139\) , \( -214622 a - 1429149\bigr] \)
28.2-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -174 a - 1159\) , \( -3170 a - 21109\bigr] \)
28.2-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -2754 a - 18339\) , \( -209802 a - 1397053\bigr] \)
28.2-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -44064 a - 293419\) , \( -13460390 a - 89631533\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph