Elliptic curve isogeny class 784.1-d over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-784.1-d
• Conductor: 784.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 784.1-d over \(\Q(\sqrt{2}) \)

Isogeny class 784.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
784.1-d1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
784.1-d2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 90 a - 94\) , \( -368 a + 642\bigr] \)
784.1-d3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -14\) , \( 10\bigr] \)
784.1-d4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -4\) , \( -6\bigr] \)
784.1-d5	\( \bigl[a\) , \( 1\) , \( 0\) , \( -90 a - 94\) , \( 368 a + 642\bigr] \)
784.1-d6	\( \bigl[a\) , \( 1\) , \( 0\) , \( -74\) , \( -286\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph