Elliptic curve isogeny class 10.4-b over number field \(\Q(\sqrt{89}) \)

• Base field: \(\Q(\sqrt{89}) \)
• Label: 2.2.89.1-10.4-b
• Conductor: 10.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 10.4-b over \(\Q(\sqrt{89}) \)

Isogeny class 10.4-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
10.4-b1	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -9\) , \( 37 a + 151\bigr] \)
10.4-b2	\( \bigl[1\) , \( -a\) , \( 1\) , \( 289 a - 1500\) , \( -5248 a + 27374\bigr] \)
10.4-b3	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -5 a - 19\) , \( 6 a + 25\bigr] \)
10.4-b4	\( \bigl[1\) , \( -a\) , \( 1\) , \( -45081 a - 190100\) , \( 11390518 a + 48033710\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph