Elliptic curve isogeny class 36.1-b over number field \(\Q(\sqrt{205}) \)

• Base field: \(\Q(\sqrt{205}) \)
• Label: 2.2.205.1-36.1-b
• Conductor: 36.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 36.1-b over \(\Q(\sqrt{205}) \)

Isogeny class 36.1-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
36.1-b1	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 17 a + 69\) , \( 53 a + 261\bigr] \)
36.1-b2	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 32 a - 46\) , \( -428 a + 3944\bigr] \)
36.1-b3	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 512 a - 3726\) , \( -15820 a + 121800\bigr] \)
36.1-b4	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 47 a - 161\) , \( 323 a - 1809\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph