Elliptic curve isogeny class 93.1-e over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-93.1-e
• Conductor: 93.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 93.1-e over \(\Q(\sqrt{33}) \)

Isogeny class 93.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
93.1-e1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -303 a + 1021\) , \( -9496 a + 32023\bigr] \)
93.1-e2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 55 a + 130\) , \( 460 a + 1091\bigr] \)
93.1-e3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 47 a - 159\) , \( 276 a - 931\bigr] \)
93.1-e4	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -3\) , \( a - 6\bigr] \)
93.1-e5	\( \bigl[1\) , \( 0\) , \( 1\) , \( 167 a - 564\) , \( -1674 a + 5645\bigr] \)
93.1-e6	\( \bigl[1\) , \( 0\) , \( 1\) , \( 2557 a - 8629\) , \( -119132 a + 401751\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph