Properties

Base field 3.3.316.1
Label 3.3.316.1-32.5-b
Conductor 32.5
Rank \( 0 \)

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Base field 3.3.316.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 4 x + 2 \); class number \(1\).

Elliptic curves in class 32.5-b over 3.3.316.1

Isogeny class 32.5-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
32.5-b1 \( \bigl[a^{2} - 3\) , \( a\) , \( a + 1\) , \( 14 a^{2} - a - 107\) , \( 81 a^{2} - 88 a - 210\bigr] \)
32.5-b2 \( \bigl[a^{2} - 3\) , \( a\) , \( a + 1\) , \( 19 a^{2} - 11 a - 82\) , \( 88 a^{2} - 49 a - 378\bigr] \)
32.5-b3 \( \bigl[a + 1\) , \( -a^{2} - a + 4\) , \( a^{2} - 3\) , \( -27 a^{2} + 70 a - 18\) , \( 127 a^{2} - 348 a + 138\bigr] \)
32.5-b4 \( \bigl[a + 1\) , \( -a^{2} - a + 4\) , \( a^{2} - 3\) , \( -2 a^{2} + 7\) , \( -a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph