Elliptic curve isogeny class 31752.3-i over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-31752.3-i
• Conductor: 31752.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 31752.3-i over \(\Q(\sqrt{-2}) \)

Isogeny class 31752.3-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
31752.3-i1	\( \bigl[a\) , \( -1\) , \( a\) , \( 4\) , \( 6\bigr] \)
31752.3-i2	\( \bigl[a\) , \( -1\) , \( a\) , \( -131\) , \( -399\bigr] \)
31752.3-i3	\( \bigl[a\) , \( -1\) , \( a\) , \( -41\) , \( 123\bigr] \)
31752.3-i4	\( \bigl[a\) , \( -1\) , \( a\) , \( -671\) , \( 7053\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph