Elliptic curve isogeny class 10.1-b over number field \(\Q(\sqrt{89}) \)

• Base field: \(\Q(\sqrt{89}) \)
• Label: 2.2.89.1-10.1-b
• Conductor: 10.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{89}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 22 \); class number \(1\).

Elliptic curves in class 10.1-b over \(\Q(\sqrt{89}) \)

Isogeny class 10.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
10.1-b1	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 45081 a - 235181\) , \( -11390518 a + 59424228\bigr] \)
10.1-b2	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 7 a - 26\) , \( -12 a + 56\bigr] \)
10.1-b3	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -289 a - 1211\) , \( 5248 a + 22126\bigr] \)
10.1-b4	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 2 a - 11\) , \( -38 a + 198\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph