Elliptic curve isogeny class 27.2-b over number field \(\Q(\sqrt{61}) \)

• Base field: \(\Q(\sqrt{61}) \)
• Label: 2.2.61.1-27.2-b
• Conductor: 27.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 27.2-b over \(\Q(\sqrt{61}) \)

Isogeny class 27.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
27.2-b1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -8 a - 24\) , \( -66 a - 228\bigr] \)
27.2-b2	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -198 a - 674\) , \( -1824 a - 6210\bigr] \)
27.2-b3	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -168 a - 569\) , \( -2673 a - 9105\bigr] \)
27.2-b4	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -2698 a - 9184\) , \( -155890 a - 530828\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph