Elliptic curve isogeny class 4.1-a over number field \(\Q(\sqrt{89}) \)

• Base field: \(\Q(\sqrt{89}) \)
• Label: 2.2.89.1-4.1-a
• Conductor: 4.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4.1-a over \(\Q(\sqrt{89}) \)

Isogeny class 4.1-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -716 a + 3738\) , \( -1996 a + 10404\bigr] \)
4.1-a2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -9585 a - 40413\) , \( -1212620 a - 5113612\bigr] \)
4.1-a3	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 9584 a - 49997\) , \( 1212619 a - 6326231\bigr] \)
4.1-a4	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 715 a + 3022\) , \( 1995 a + 8408\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph