Elliptic curve isogeny class 242.3-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-242.3-a
• Conductor: 242.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 242.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 242.3-a contains 4 curves linked by isogenies of degrees dividing 33.

Curve label	Weierstrass Coefficients
242.3-a1	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -41 a - 13\) , \( -109 a + 122\bigr] \)
242.3-a2	\( \bigl[1\) , \( 1\) , \( a\) , \( 7 a - 41\) , \( 29 a - 121\bigr] \)
242.3-a3	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 9 a + 13\) , \( 10 a + 40\bigr] \)
242.3-a4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -35 a - 194\) , \( 268 a + 938\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 33 & 11 \\ 3 & 1 & 11 & 33 \\ 33 & 11 & 1 & 3 \\ 11 & 33 & 3 & 1 \end{array}\right)\)

Isogeny graph