Elliptic curve isogeny class 288.5-b over number field \(\Q(\sqrt{-39}) \)

• Base field: \(\Q(\sqrt{-39}) \)
• Label: 2.0.39.1-288.5-b
• Conductor: 288.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 288.5-b over \(\Q(\sqrt{-39}) \)

Isogeny class 288.5-b contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
288.5-b1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 16378\) , \( 264058 a - 123840\bigr] \)
288.5-b2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -67 a + 1046\) , \( 4690 a - 7468\bigr] \)
288.5-b3	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -3009 a + 1320\) , \( 121386 a - 74164\bigr] \)
288.5-b4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 182\) , \( -182 a\bigr] \)
288.5-b5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 778\) , \( -758 a + 768\bigr] \)
288.5-b6	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 366 a - 165\) , \( -3570 a - 9904\bigr] \)
288.5-b7	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 8 a - 139\) , \( -131 a + 563\bigr] \)
288.5-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