Elliptic curve isogeny class 252.2-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-252.2-a
• Conductor: 252.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 252.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 252.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
252.2-a1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -3 a - 9\) , \( 5 a + 5\bigr] \)
252.2-a2	\( \bigl[1\) , \( a\) , \( a\) , \( 2 a - 11\) , \( -6 a + 11\bigr] \)
252.2-a3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \)
252.2-a4	\( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \)
252.2-a5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \)
252.2-a6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \)
252.2-a7	\( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \)
252.2-a8	\( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 16 & 8 & 16 & 4 & 8 \\ 4 & 1 & 2 & 16 & 8 & 16 & 4 & 8 \\ 2 & 2 & 1 & 8 & 4 & 8 & 2 & 4 \\ 16 & 16 & 8 & 1 & 2 & 4 & 4 & 8 \\ 8 & 8 & 4 & 2 & 1 & 2 & 2 & 4 \\ 16 & 16 & 8 & 4 & 2 & 1 & 4 & 8 \\ 4 & 4 & 2 & 4 & 2 & 4 & 1 & 2 \\ 8 & 8 & 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph