Elliptic curve isogeny class 121.1-i over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-121.1-i
• Conductor: 121.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{33}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 8 \); class number \(1\).

Elliptic curves in class 121.1-i over \(\Q(\sqrt{33}) \)

Isogeny class 121.1-i contains 4 curves linked by isogenies of degrees dividing 22.

Curve label	Weierstrass Coefficients
121.1-i1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 132 a - 459\) , \( 1521 a - 5074\bigr] \)
121.1-i2	\( \bigl[1\) , \( 0\) , \( a\) , \( -1381 a - 3275\) , \( -83691 a - 198540\bigr] \)
121.1-i3	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -30 a - 75\) , \( -215 a - 504\bigr] \)
121.1-i4	\( \bigl[1\) , \( 0\) , \( a\) , \( 7000 a - 23608\) , \( 541086 a - 1824697\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 11 & 22 & 2 \\ 11 & 1 & 2 & 22 \\ 22 & 2 & 1 & 11 \\ 2 & 22 & 11 & 1 \end{array}\right)\)

Isogeny graph