Elliptic curve isogeny class 40401.4-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-40401.4-a
• Conductor: 40401.4
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 40401.4-a over \(\Q(\sqrt{-11}) \)

Isogeny class 40401.4-a contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
40401.4-a1	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -205 a + 43\) , \( 1245 a - 1654\bigr] \)
40401.4-a2	\( \bigl[1\) , \( a\) , \( a\) , \( -194 a - 27\) , \( -1591 a + 1497\bigr] \)
40401.4-a3	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -10 a + 33\) , \( 103 a + 16\bigr] \)
40401.4-a4	\( \bigl[1\) , \( a\) , \( a\) , \( -379 a + 558\) , \( -2554 a - 6741\bigr] \)
40401.4-a5	\( \bigl[1\) , \( a\) , \( a\) , \( a - 37\) , \( -53 a + 152\bigr] \)
40401.4-a6	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -215 a - 532\) , \( -2139 a - 7696\bigr] \)
40401.4-a7	\( \bigl[1\) , \( a\) , \( a\) , \( -3129 a - 452\) , \( -95320 a + 86415\bigr] \)
40401.4-a8	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -3315 a + 778\) , \( 81337 a - 118792\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph