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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-5202.5-g
• 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-g over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.5-g contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
5202.5-g1	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 89 a - 137\) , \( -532 a + 213\bigr] \)
5202.5-g2	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 29 a - 57\) , \( 100 a - 131\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph