Elliptic curve isogeny class 4356.6-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4356.6-b
• Conductor: 4356.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 4356.6-b over \(\Q(\sqrt{-7}) \)

Isogeny class 4356.6-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
4356.6-b1	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -3 a + 2\) , \( 45 a + 2\bigr] \)
4356.6-b2	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 12 a + 20\) , \( 6 a - 20\bigr] \)
4356.6-b3	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -30\) , \( 18 a + 30\bigr] \)
4356.6-b4	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 157 a - 138\) , \( 805 a - 58\bigr] \)
4356.6-b5	\( \bigl[1\) , \( -a\) , \( 1\) , \( -46 a + 9\) , \( 135 a - 178\bigr] \)
4356.6-b6	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -33 a + 60\) , \( 45 a + 198\bigr] \)
4356.6-b7	\( \bigl[1\) , \( -a\) , \( 1\) , \( -736 a + 159\) , \( 8283 a - 10030\bigr] \)
4356.6-b8	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -543 a + 960\) , \( 3123 a + 10482\bigr] \)

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