Elliptic curve isogeny class 5202.4-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-5202.4-b
• Conductor: 5202.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 5202.4-b over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.4-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
5202.4-b1	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -5773 a - 561\) , \( 137153 a - 442749\bigr] \)
5202.4-b2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 87 a - 86\) , \( 446 a + 48\bigr] \)
5202.4-b3	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 312 a - 466\) , \( -3501 a + 3002\bigr] \)
5202.4-b4	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -6673 a + 959\) , \( 150309 a - 291157\bigr] \)

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