Elliptic curve isogeny class 41472.3-f over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41472.3-f
• Conductor: 41472.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 41472.3-f over \(\Q(\sqrt{-2}) \)

Isogeny class 41472.3-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
41472.3-f1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -48 a - 42\) , \( -196 a - 8\bigr] \)
41472.3-f2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 3\) , \( -7 a - 8\bigr] \)
41472.3-f3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 42 a + 3\) , \( -70 a - 134\bigr] \)
41472.3-f4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -48 a + 93\) , \( -196 a - 386\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph