Elliptic curve isogeny class 1800.1-d over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1800.1-d
• Conductor: 1800.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1800.1-d over \(\Q(\sqrt{2}) \)

Isogeny class 1800.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1800.1-d1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -20\) , \( -300\bigr] \)
1800.1-d2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 20\) , \( 10\bigr] \)
1800.1-d3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -5\) , \( 0\bigr] \)
1800.1-d4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -50\) , \( -144\bigr] \)
1800.1-d5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \)
1800.1-d6	\( \bigl[a\) , \( 0\) , \( 0\) , \( -800\) , \( -8844\bigr] \)

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