Elliptic curve isogeny class 20.1-a over number field \(\Q(\sqrt{205}) \)

• Base field: \(\Q(\sqrt{205}) \)
• Label: 2.2.205.1-20.1-a
• Conductor: 20.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 20.1-a over \(\Q(\sqrt{205}) \)

Isogeny class 20.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
20.1-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 4655 a + 30997\) , \( 2978860 a + 19835962\bigr] \)
20.1-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -6545 a - 43583\) , \( 734100 a + 4888306\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph