Elliptic curve isogeny class 16.4-b over number field \(\Q(\sqrt{41}) \)

• Base field: \(\Q(\sqrt{41}) \)
• Label: 2.2.41.1-16.4-b
• Conductor: 16.4
• Rank: \( 1 \)

Base field \(\Q(\sqrt{41}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 10 \); class number \(1\).

Elliptic curves in class 16.4-b over \(\Q(\sqrt{41}) \)

Isogeny class 16.4-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
16.4-b1	\( \bigl[a\) , \( -1\) , \( a\) , \( -2 a - 9\) , \( -13 a - 37\bigr] \)
16.4-b2	\( \bigl[a\) , \( 1\) , \( a\) , \( 1300 a + 3511\) , \( 3153 a + 8517\bigr] \)
16.4-b3	\( \bigl[a\) , \( 1\) , \( a\) , \( -325 a - 879\) , \( -325 a - 879\bigr] \)
16.4-b4	\( \bigl[a\) , \( 1\) , \( a\) , \( 5 a - 19\) , \( 5 a - 19\bigr] \)
16.4-b5	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
16.4-b6	\( \bigl[a\) , \( 1\) , \( a\) , \( -20 a + 71\) , \( -17 a + 57\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph