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

• Base field: \(\Q(\sqrt{205}) \)
• Label: 2.2.205.1-12.2-b
• Conductor: 12.2
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
12.2-b1	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 14 a - 88\) , \( 93 a - 753\bigr] \)
12.2-b2	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 44 a - 318\) , \( -255 a + 1913\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph