Elliptic curve isogeny class 20.1-a over number field \(\Q(\sqrt{61}) \)

• Base field: \(\Q(\sqrt{61}) \)
• Label: 2.2.61.1-20.1-a
• Conductor: 20.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 20.1-a over \(\Q(\sqrt{61}) \)

Isogeny class 20.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
20.1-a1	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -4 a\) , \( -2 a + 6\bigr] \)
20.1-a2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -2 a + 12\) , \( -7 a + 38\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph