Elliptic curve isogeny class 36.1-b over number field \(\Q(\sqrt{105}) \)

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-36.1-b
• Conductor: 36.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{105}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 26 \); class number \(2\).

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 36.1-b over \(\Q(\sqrt{105}) \)

Isogeny class 36.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
36.1-b1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3\) , \( -1449 a + 8136\bigr] \)
36.1-b2	\( \bigl[1\) , \( -1\) , \( a\) , \( 30499 a - 171513\) , \( -6570718 a + 36950263\bigr] \)
36.1-b3	\( \bigl[1\) , \( -1\) , \( a\) , \( 487999 a - 2744253\) , \( -420146386 a + 2362682851\bigr] \)
36.1-b4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 900 a - 5163\) , \( -30285 a + 169776\bigr] \)