Elliptic curve isogeny class 14112.2-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-14112.2-b
• Conductor: 14112.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 14112.2-b over \(\Q(\sqrt{-2}) \)

Isogeny class 14112.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14112.2-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( 13\) , \( -22\bigr] \)
14112.2-b2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -22\) , \( 40\bigr] \)
14112.2-b3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -28\) , \( 49\bigr] \)
14112.2-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -84\) , \( -270\bigr] \)

Rank

Rank: \( 1 \)

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