Elliptic curve isogeny class 12.2-a over number field \(\Q(\sqrt{205}) \)

• Base field: \(\Q(\sqrt{205}) \)
• Label: 2.2.205.1-12.2-a
• Conductor: 12.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 12.2-a over \(\Q(\sqrt{205}) \)

Isogeny class 12.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12.2-a1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 12 a + 61\) , \( 29 a + 182\bigr] \)
12.2-a2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -18 a - 139\) , \( 35 a + 222\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph