Elliptic curve isogeny class 13824.3-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-13824.3-d
• Conductor: 13824.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 13824.3-d over \(\Q(\sqrt{-2}) \)

Isogeny class 13824.3-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
13824.3-d1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 14 a - 17\) , \( 47 a - 9\bigr] \)
13824.3-d2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a - 2\) , \( 2 a\bigr] \)
13824.3-d3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 18\) , \( 10 a + 22\bigr] \)
13824.3-d4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -16 a - 32\) , \( 56 a + 36\bigr] \)

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