Elliptic curve isogeny class 35.1-a over number field \(\Q(\sqrt{105}) \)

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-35.1-a
• Conductor: 35.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 35.1-a over \(\Q(\sqrt{105}) \)

Isogeny class 35.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
35.1-a1	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -86155 a - 398325\) , \( -32460825 a - 150081819\bigr] \)
35.1-a2	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -875 a - 4035\) , \( 36705 a + 169711\bigr] \)
35.1-a3	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 5685 a + 26295\) , \( -98901 a - 457260\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph