Elliptic curve isogeny class 46.2-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-46.2-a
• Conductor: 46.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 46.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 46.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
46.2-a1	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -4\) , \( -1\bigr] \)
46.2-a2	\( \bigl[1\) , \( -a\) , \( a\) , \( -6 a + 10\) , \( 2 a + 8\bigr] \)
46.2-a3	\( \bigl[1\) , \( -a\) , \( a\) , \( -a + 10\) , \( -8 a + 30\bigr] \)
46.2-a4	\( \bigl[1\) , \( -a\) , \( a\) , \( -a\) , \( 0\bigr] \)
46.2-a5	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a - 2\) , \( -a + 1\bigr] \)
46.2-a6	\( \bigl[1\) , \( -a\) , \( a\) , \( -91 a + 170\) , \( 240 a + 618\bigr] \)

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