Elliptic curve isogeny class 28672.7-j over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-28672.7-j
• Conductor: 28672.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 28672.7-j over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.7-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
28672.7-j1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a - 2\) , \( -9 a + 22\bigr] \)
28672.7-j2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a + 17\) , \( -17 a + 11\bigr] \)
28672.7-j3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -43 a + 137\) , \( 279 a + 211\bigr] \)
28672.7-j4	\( \bigl[0\) , \( a\) , \( 0\) , \( 42 a - 7\) , \( -37 a - 156\bigr] \)

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