Elliptic curve isogeny class 22400.2-j over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-22400.2-j
• Conductor: 22400.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 22400.2-j over \(\Q(\sqrt{-7}) \)

Isogeny class 22400.2-j contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
22400.2-j1	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -45 a + 60\) , \( 23 a + 173\bigr] \)
22400.2-j2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 9 a - 72\) , \( 53 a - 199\bigr] \)
22400.2-j3	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 12 a + 6\) , \( -47 a + 17\bigr] \)
22400.2-j4	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -88 a - 34\) , \( -319 a + 113\bigr] \)
22400.2-j5	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -438 a - 174\) , \( 5393 a - 1903\bigr] \)
22400.2-j6	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1338 a - 534\) , \( -27519 a + 9713\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 4 & 8 & 8 \\ 4 & 1 & 2 & 4 & 8 & 8 \\ 2 & 2 & 1 & 2 & 4 & 4 \\ 4 & 4 & 2 & 1 & 2 & 2 \\ 8 & 8 & 4 & 2 & 1 & 4 \\ 8 & 8 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph