Elliptic curve isogeny class 32.1-b over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-32.1-b
• Conductor: 32.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{22}) \)

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

Elliptic curves in class 32.1-b over \(\Q(\sqrt{22}) \)

Isogeny class 32.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
32.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
32.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -16548 a - 77617\) , \( 0\bigr] \)
32.1-b3	\( \bigl[a\) , \( -1\) , \( a\) , \( -7\) , \( -8\bigr] \)
32.1-b4	\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph