Elliptic curve isogeny class 100.1-b over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-100.1-b
• Conductor: 100.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 100.1-b over \(\Q(\sqrt{22}) \)

Isogeny class 100.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-b1	\( \bigl[a\) , \( 0\) , \( a\) , \( -10\) , \( 0\bigr] \)
100.1-b2	\( \bigl[a\) , \( 0\) , \( a\) , \( 0\) , \( 2\bigr] \)
100.1-b3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -22064 a - 103489\) , \( -2663598 a - 12493382\bigr] \)
100.1-b4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -683984 a - 3208169\) , \( 666489082 a + 3126110894\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph