Elliptic curve isogeny class 4096.7-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4096.7-b
• Conductor: 4096.7
• Rank: \( 1 \)

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

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

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

Elliptic curves in class 4096.7-b over \(\Q(\sqrt{-7}) \)

Isogeny class 4096.7-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4096.7-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 43 a - 2\) , \( 23 a + 182\bigr] \)
4096.7-b2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 6 a + 3\) , \( -a + 9\bigr] \)
4096.7-b3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a - 2\) , \( -a + 6\bigr] \)
4096.7-b4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a + 5\) , \( -5 a + 7\bigr] \)