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

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-121.1-e
• Conductor: 121.1
• Rank: \( 1 \)

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

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

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

Isogeny class 121.1-e contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
121.1-e1	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 688189 a - 2322636\) , \( 526275039 a - 1774717815\bigr] \)
121.1-e2	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 909 a - 3066\) , \( 44829 a - 151175\bigr] \)
121.1-e3	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 29 a - 96\) , \( -381 a + 1285\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph