Elliptic curve isogeny class 5202.1-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-5202.1-b
• Conductor: 5202.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 5202.1-b over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
5202.1-b1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 55 a - 68\) , \( -228 a + 72\bigr] \)
5202.1-b2	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 78 a + 55\) , \( 73 a + 569\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph