Elliptic curve isogeny class 3.2-b over number field \(\Q(\sqrt{85}) \)

• Base field: \(\Q(\sqrt{85}) \)
• Label: 2.2.85.1-3.2-b
• Conductor: 3.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 3.2-b over \(\Q(\sqrt{85}) \)

Isogeny class 3.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
3.2-b1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -13050 a - 53636\) , \( -1785556 a - 7338231\bigr] \)
3.2-b2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 245 a + 1004\) , \( -10714 a - 44034\bigr] \)
3.2-b3	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -165 a - 681\) , \( -2743 a - 11275\bigr] \)
3.2-b4	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -13055 a - 53656\) , \( -1784186 a - 7332600\bigr] \)

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