Elliptic curve isogeny class 238.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-238.1-c
• Number of curves: 6
• Conductor: 238.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 238.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 238.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
238.1-c1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -2 a - 1\) , \( -a + 1\bigr] \)
238.1-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -17 a + 79\) , \( 467 a - 479\bigr] \)
238.1-c3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 18 a - 51\) , \( 99 a - 103\bigr] \)
238.1-c4	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 373 a - 661\) , \( 5459 a - 8231\bigr] \)
238.1-c5	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -2 a - 21\) , \( 7 a + 33\bigr] \)
238.1-c6	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -22 a - 311\) , \( 267 a + 2137\bigr] \)