Elliptic curve isogeny class 847.2-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-847.2-c
• Conductor: 847.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 847.2-c over \(\Q(\sqrt{-7}) \)

Isogeny class 847.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
847.2-c1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 12 a - 19\) , \( -27 a + 9\bigr] \)
847.2-c2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -13 a - 6\) , \( 26 a - 17\bigr] \)
847.2-c3	\( \bigl[1\) , \( 1\) , \( 0\) , \( 4\) , \( 11\bigr] \)
847.2-c4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -51\) , \( 110\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph