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

• Base field: \(\Q(\sqrt{85}) \)
• Label: 2.2.85.1-3.2-a
• Conductor: 3.2
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
3.2-a1	\( \bigl[a\) , \( a\) , \( 0\) , \( -10332 a - 42522\) , \( -1271183 a - 5224453\bigr] \)
3.2-a2	\( \bigl[a\) , \( a\) , \( 0\) , \( 198 a + 813\) , \( -7340 a - 30166\bigr] \)
3.2-a3	\( \bigl[a\) , \( a\) , \( 0\) , \( -127 a - 522\) , \( -2077 a - 8536\bigr] \)
3.2-a4	\( \bigl[a\) , \( a\) , \( 0\) , \( -10342 a - 42507\) , \( -1270240 a - 5220400\bigr] \)

Rank

Rank: \( 0 \)

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