Elliptic curve isogeny class 5202.5-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-5202.5-e
• Conductor: 5202.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 5202.5-e over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.5-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
5202.5-e1	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 1776 a - 186\) , \( -26138 a - 30473\bigr] \)
5202.5-e2	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -9 a + 4\) , \( -15\bigr] \)
5202.5-e3	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -9 a - 16\) , \( -28 a - 63\bigr] \)
5202.5-e4	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 111 a - 6\) , \( -398 a - 431\bigr] \)
5202.5-e5	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 366 a + 334\) , \( -738 a + 5859\bigr] \)
5202.5-e6	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -129 a - 346\) , \( -1450 a - 2367\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph