Elliptic curve isogeny class 8.1-a over number field \(\Q(\sqrt{305}) \)

• Base field: \(\Q(\sqrt{305}) \)
• Label: 2.2.305.1-8.1-a
• Conductor: 8.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{305}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 76 \); class number \(2\).

Elliptic curves in class 8.1-a over \(\Q(\sqrt{305}) \)

Isogeny class 8.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
8.1-a1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -777 a - 6168\) , \( 31293 a + 258272\bigr] \)
8.1-a2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 2928 a + 24332\) , \( 180300 a + 1484916\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph