Elliptic curve isogeny class 5625.3-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-5625.3-a
• Conductor: 5625.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 5625.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 5625.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
5625.3-a1	\( \bigl[a\) , \( -1\) , \( 1\) , \( 62 a + 182\) , \( 625 a - 716\bigr] \)
5625.3-a2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -63 a + 8\) , \( -188 a + 622\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph