Elliptic curve isogeny class 322.4-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-322.4-b
• Conductor: 322.4
• Rank: \( 0 \)

Base field \(\Q(\sqrt{2}) \)

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

Rank

Rank: \( 0 \)

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

Elliptic curves in class 322.4-b over \(\Q(\sqrt{2}) \)

Isogeny class 322.4-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
322.4-b1	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -462 a - 795\) , \( -24731 a - 35605\bigr] \)
322.4-b2	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 22 a - 27\) , \( 49 a - 57\bigr] \)
322.4-b3	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 2 a - 7\) , \( -7 a + 11\bigr] \)
322.4-b4	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 82 a - 182\) , \( 554 a - 1002\bigr] \)