Elliptic curve isogeny class 288.2-b over number field \(\Q(\sqrt{-39}) \)

• Base field: \(\Q(\sqrt{-39}) \)
• Label: 2.0.39.1-288.2-b
• Conductor: 288.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-39}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 10 \); class number \(4\).

Elliptic curves in class 288.2-b over \(\Q(\sqrt{-39}) \)

Isogeny class 288.2-b contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
288.2-b1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 16378\) , \( -264058 a + 123840\bigr] \)
288.2-b2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 3007 a - 1687\) , \( -121387 a + 47223\bigr] \)
288.2-b3	\( \bigl[a\) , \( a\) , \( 0\) , \( 65 a + 986\) , \( -3703 a - 4430\bigr] \)
288.2-b4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 182\) , \( 182 a\bigr] \)
288.2-b5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 778\) , \( 758 a - 768\bigr] \)
288.2-b6	\( \bigl[a\) , \( a\) , \( 0\) , \( -10 a - 124\) , \( 8 a + 640\bigr] \)
288.2-b7	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -368 a + 203\) , \( 3569 a - 13473\bigr] \)
288.2-b8	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 262138\) , \( -16631674 a + 8184768\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 2 & 5 & 10 & 10 & 10 & 2 \\ 2 & 1 & 4 & 10 & 20 & 20 & 5 & 4 \\ 2 & 4 & 1 & 10 & 20 & 5 & 20 & 4 \\ 5 & 10 & 10 & 1 & 2 & 2 & 2 & 10 \\ 10 & 20 & 20 & 2 & 1 & 4 & 4 & 5 \\ 10 & 20 & 5 & 2 & 4 & 1 & 4 & 20 \\ 10 & 5 & 20 & 2 & 4 & 4 & 1 & 20 \\ 2 & 4 & 4 & 10 & 5 & 20 & 20 & 1 \end{array}\right)\)

Isogeny graph