Elliptic curve isogeny class 28.1-a over number field \(\Q(\sqrt{105}) \)

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-28.1-a
• Conductor: 28.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 28.1-a over \(\Q(\sqrt{105}) \)

Isogeny class 28.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
28.1-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 1877 a - 10553\) , \( -96600 a + 543228\bigr] \)
28.1-a2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 7 a - 13\) , \( 48 a - 244\bigr] \)
28.1-a3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -48 a + 297\) , \( -819 a + 4634\bigr] \)
28.1-a4	\( \bigl[a\) , \( 1\) , \( 0\) , \( 392 a - 2183\) , \( -6987 a + 39306\bigr] \)
28.1-a5	\( \bigl[a\) , \( 1\) , \( 0\) , \( 117 a - 633\) , \( 1782 a - 10000\bigr] \)
28.1-a6	\( \bigl[a\) , \( 1\) , \( 0\) , \( 30037 a - 169273\) , \( -6361944 a + 35778044\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph