Elliptic curve isogeny class 16.2-a over number field \(\Q(\sqrt{41}) \)

• Base field: \(\Q(\sqrt{41}) \)
• Label: 2.2.41.1-16.2-a
• Conductor: 16.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 16.2-a over \(\Q(\sqrt{41}) \)

Isogeny class 16.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
16.2-a1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -104 a - 280\) , \( 912 a + 2464\bigr] \)
16.2-a2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( a + 5\) , \( -a + 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph