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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-13824.3-s
• Conductor: 13824.3
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
13824.3-s1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 14 a - 17\) , \( -47 a + 9\bigr] \)
13824.3-s2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a - 2\) , \( -2 a\bigr] \)
13824.3-s3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a + 18\) , \( -10 a - 22\bigr] \)
13824.3-s4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -16 a - 32\) , \( -56 a - 36\bigr] \)

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