Elliptic curve isogeny class 12544.5-g over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-12544.5-g
• Conductor: 12544.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 12544.5-g over \(\Q(\sqrt{-7}) \)

Isogeny class 12544.5-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
12544.5-g1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1493 a - 1790\) , \( 31268 a - 12632\bigr] \)
12544.5-g2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -278 a + 100\) , \( -1637 a + 2594\bigr] \)
12544.5-g3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 93 a - 110\) , \( 524 a - 200\bigr] \)
12544.5-g4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -149 a - 185\) , \( -1884 a + 488\bigr] \)
12544.5-g5	\( \bigl[0\) , \( a\) , \( 0\) , \( -37 a + 39\) , \( -20 a + 380\bigr] \)
12544.5-g6	\( \bigl[0\) , \( -a\) , \( 0\) , \( -9 a + 95\) , \( -260 a - 72\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph