Elliptic curve isogeny class 2744.1-f over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2744.1-f
• Conductor: 2744.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2744.1-f over \(\Q(\sqrt{2}) \)

Isogeny class 2744.1-f contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
2744.1-f1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -109 a - 243\) , \( 1684 a + 2062\bigr] \)
2744.1-f2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 61 a + 17\) , \( 66 a + 308\bigr] \)
2744.1-f3	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -9 a - 18\) , \( 3 a + 7\bigr] \)
2744.1-f4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 7\) , \( -66 a + 92\bigr] \)
2744.1-f5	\( \bigl[a\) , \( 0\) , \( a\) , \( 81 a - 129\) , \( 141 a - 183\bigr] \)
2744.1-f6	\( \bigl[a\) , \( 0\) , \( a\) , \( -409 a + 361\) , \( 1317 a - 673\bigr] \)

Rank

Rank: \( 1 \)

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