Elliptic curve isogeny class 28224.1-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-28224.1-d
• Conductor: 28224.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 28224.1-d over \(\Q(\sqrt{-7}) \)

Isogeny class 28224.1-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
28224.1-d1	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1190 a + 476\) , \( 7595 a - 94178\bigr] \)
28224.1-d2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -35 a - 14\) , \( 0\bigr] \)
28224.1-d3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 140 a + 56\) , \( 35 a - 434\bigr] \)
28224.1-d4	\( \bigl[a\) , \( 1\) , \( a\) , \( 40 a - 162\) , \( 275 a - 795\bigr] \)
28224.1-d5	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1365 a + 546\) , \( -3150 a + 39060\bigr] \)
28224.1-d6	\( \bigl[a\) , \( a\) , \( a\) , \( -86 a + 145\) , \( -130 a - 556\bigr] \)
28224.1-d7	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1715 a + 686\) , \( 4760 a - 59024\bigr] \)
28224.1-d8	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 27440 a + 10976\) , \( 298025 a - 3695510\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph