Elliptic curve isogeny class 1.1-a over number field \(\Q(\sqrt{41}) \)

• Base field: \(\Q(\sqrt{41}) \)
• Label: 2.2.41.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1.1-a over \(\Q(\sqrt{41}) \)

Isogeny class 1.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[1\) , \( a\) , \( a\) , \( 3\) , \( -2\bigr] \)
1.1-a2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 40 a + 108\) , \( 10 a + 27\bigr] \)
1.1-a3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -10 a - 27\) , \( 0\bigr] \)
1.1-a4	\( \bigl[1\) , \( 0\) , \( 0\) , \( 10 a - 37\) , \( 0\bigr] \)
1.1-a5	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a + 3\) , \( -a - 2\bigr] \)
1.1-a6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -40 a + 148\) , \( -10 a + 37\bigr] \)

Rank

Rank: \( 0 \)

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