Elliptic curve isogeny class 5202.6-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-5202.6-c
• Conductor: 5202.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 5202.6-c over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.6-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
5202.6-c1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 43 a + 476\) , \( 4872 a + 1842\bigr] \)
5202.6-c2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3 a - 9\) , \( -9\bigr] \)
5202.6-c3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 18 a - 29\) , \( -69 a + 15\bigr] \)
5202.6-c4	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -17 a + 556\) , \( 3860 a + 290\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 5 & 2 \\ 10 & 1 & 2 & 5 \\ 5 & 2 & 1 & 10 \\ 2 & 5 & 10 & 1 \end{array}\right)\)

Isogeny graph