Elliptic curve isogeny class 80.1-b over number field \(\Q(\sqrt{65}) \)

• Base field: \(\Q(\sqrt{65}) \)
• Label: 2.2.65.1-80.1-b
• Conductor: 80.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{65}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 16 \); class number \(2\).

Elliptic curves in class 80.1-b over \(\Q(\sqrt{65}) \)

Isogeny class 80.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
80.1-b1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 65945 a - 298805\) , \( 28064795 a - 127165203\bigr] \)
80.1-b2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -6655 a + 30155\) , \( -599525 a + 2716525\bigr] \)
80.1-b3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 2420 a - 10965\) , \( -90255 a + 408957\bigr] \)
80.1-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 75020 a - 339925\) , \( 22426525 a - 101617475\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph