Properties

Base field \(\Q(\sqrt{85}) \)
Label 2.2.85.1-3.2-a
Conductor 3.2
Rank not recorded

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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 not yet determined.

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