Elliptic curve isogeny class 9.1-a over number field \(\Q(\sqrt{55}) \)

• Base field: \(\Q(\sqrt{55}) \)
• Label: 2.2.220.1-9.1-a
• Conductor: 9.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{55}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 55 \); class number \(2\).

Elliptic curves in class 9.1-a over \(\Q(\sqrt{55}) \)

Isogeny class 9.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9.1-a1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -2 a + 1\) , \( 31 a + 211\bigr] \)
9.1-a2	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -127 a - 954\) , \( -662 a - 4928\bigr] \)
9.1-a3	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -82 a - 594\) , \( 868 a + 6421\bigr] \)
9.1-a4	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -1317 a - 9754\) , \( 67086 a + 497510\bigr] \)

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