Elliptic curve isogeny class 8.3-a over number field \(\Q(\sqrt{41}) \)

• Base field: \(\Q(\sqrt{41}) \)
• Label: 2.2.41.1-8.3-a
• Conductor: 8.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 8.3-a over \(\Q(\sqrt{41}) \)

Isogeny class 8.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
8.3-a1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 19 a - 53\) , \( 45 a - 143\bigr] \)
8.3-a2	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -101 a - 273\) , \( -1337 a - 3613\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph