Elliptic curve isogeny class 1152.2-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-1152.2-a
• Conductor: 1152.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1152.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 1152.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
1152.2-a1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2 a\) , \( 4 a - 40\bigr] \)
1152.2-a2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -7 a + 24\) , \( a - 15\bigr] \)
1152.2-a3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 11 a - 20\) , \( a - 15\bigr] \)
1152.2-a4	\( \bigl[a\) , \( -1\) , \( 0\) , \( 98 a + 40\) , \( 24 a - 800\bigr] \)
1152.2-a5	\( \bigl[a\) , \( a\) , \( 0\) , \( -16 a - 33\) , \( -76 a - 39\bigr] \)
1152.2-a6	\( \bigl[a\) , \( 1\) , \( 0\) , \( -34 a + 12\) , \( 64 a - 96\bigr] \)
1152.2-a7	\( \bigl[a\) , \( a\) , \( 0\) , \( -256 a - 513\) , \( -4060 a - 3399\bigr] \)
1152.2-a8	\( \bigl[a\) , \( 1\) , \( 0\) , \( -544 a + 192\) , \( 4498 a - 6540\bigr] \)

Rank

Rank: \( 0 \)

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