Elliptic curve isogeny class 25.1-a over number field \(\Q(\sqrt{61}) \)

• Base field: \(\Q(\sqrt{61}) \)
• Label: 2.2.61.1-25.1-a
• Conductor: 25.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{61}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 15 \); class number \(1\).

Elliptic curves in class 25.1-a over \(\Q(\sqrt{61}) \)

Isogeny class 25.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
25.1-a1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 530 a + 1810\) , \( -43920 a - 149549\bigr] \)
25.1-a2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -445 a - 1510\) , \( -9069 a - 30877\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph