Elliptic curve isogeny class 46.3-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-46.3-a
• Conductor: 46.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 46.3-a over \(\Q(\sqrt{-7}) \)

Isogeny class 46.3-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
46.3-a1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( a - 4\) , \( -a - 4\bigr] \)
46.3-a2	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 5 a + 4\) , \( -3 a + 10\bigr] \)
46.3-a3	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 9\) , \( 7 a + 22\bigr] \)
46.3-a4	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -1\) , \( -a\bigr] \)
46.3-a5	\( \bigl[1\) , \( -a\) , \( a\) , \( -2\) , \( 1\bigr] \)
46.3-a6	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 90 a + 79\) , \( -241 a + 858\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph