Elliptic curve isogeny class 80.1-a over number field \(\Q(\sqrt{85}) \)

• Base field: \(\Q(\sqrt{85}) \)
• Label: 2.2.85.1-80.1-a
• Conductor: 80.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{85}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 21 \); class number \(2\).

Elliptic curves in class 80.1-a over \(\Q(\sqrt{85}) \)

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

Curve label	Weierstrass Coefficients
80.1-a1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 400 a - 2064\) , \( 14884 a - 76100\bigr] \)
80.1-a2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -40 a + 216\) , \( -364 a + 1852\bigr] \)
80.1-a3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 15 a - 69\) , \( -26 a + 130\bigr] \)
80.1-a4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 455 a - 2349\) , \( 12086 a - 61778\bigr] \)

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