Elliptic curve isogeny class 10.2-a over number field \(\Q(\sqrt{41}) \)

• Base field: \(\Q(\sqrt{41}) \)
• Label: 2.2.41.1-10.2-a
• Conductor: 10.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.2-a over \(\Q(\sqrt{41}) \)

Isogeny class 10.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
10.2-a1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -306 a - 826\) , \( -7026 a - 18984\bigr] \)
10.2-a2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 29 a + 79\) , \( 128 a + 343\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph