Elliptic curve isogeny class 4356.4-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4356.4-d
• Conductor: 4356.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 4356.4-d over \(\Q(\sqrt{-7}) \)

Isogeny class 4356.4-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
4356.4-d1	\( \bigl[1\) , \( -a\) , \( 0\) , \( 3 a - 1\) , \( -45 a + 47\bigr] \)
4356.4-d2	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 2 a - 31\) , \( -17 a + 17\bigr] \)
4356.4-d3	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -10 a + 31\) , \( -17 a + 17\bigr] \)
4356.4-d4	\( \bigl[1\) , \( -a\) , \( 0\) , \( -157 a + 19\) , \( -805 a + 747\bigr] \)
4356.4-d5	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 35 a + 25\) , \( -79 a + 217\bigr] \)
4356.4-d6	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 46 a - 37\) , \( -135 a - 43\bigr] \)
4356.4-d7	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 545 a + 415\) , \( -3667 a + 13189\bigr] \)
4356.4-d8	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 736 a - 577\) , \( -8283 a - 1747\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 4 & 2 & 2 & 2 & 4 & 4 \\ 4 & 1 & 16 & 8 & 8 & 2 & 16 & 4 \\ 4 & 16 & 1 & 8 & 2 & 8 & 4 & 16 \\ 2 & 8 & 8 & 1 & 4 & 4 & 8 & 8 \\ 2 & 8 & 2 & 4 & 1 & 4 & 2 & 8 \\ 2 & 2 & 8 & 4 & 4 & 1 & 8 & 2 \\ 4 & 16 & 4 & 8 & 2 & 8 & 1 & 16 \\ 4 & 4 & 16 & 8 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph