Elliptic curve isogeny class 18144.5-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-18144.5-a
• Conductor: 18144.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 18144.5-a over \(\Q(\sqrt{-7}) \)

Isogeny class 18144.5-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
18144.5-a1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 192 a + 576\) , \( -4560 a + 6260\bigr] \)
18144.5-a2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 21 a - 126\) , \( 106 a - 574\bigr] \)
18144.5-a3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 12 a + 36\) , \( -60 a + 104\bigr] \)
18144.5-a4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 69 a - 87\) , \( 345 a - 431\bigr] \)
18144.5-a5	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -3 a - 15\) , \( -29 a - 45\bigr] \)
18144.5-a6	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -21 a + 3\) , \( 39 a - 17\bigr] \)

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