Elliptic curve isogeny class 68.1-a over number field \(\Q(\sqrt{85}) \)

• Base field: \(\Q(\sqrt{85}) \)
• Label: 2.2.85.1-68.1-a
• Conductor: 68.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 68.1-a over \(\Q(\sqrt{85}) \)

Isogeny class 68.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
68.1-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 31 a - 176\) , \( -80 a + 399\bigr] \)
68.1-a2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 1241 a - 6446\) , \( 38090 a - 194961\bigr] \)
68.1-a3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 471 a - 2456\) , \( -11288 a + 57711\bigr] \)
68.1-a4	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 1131 a - 5876\) , \( 47164 a - 241377\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph