Properties

Base field 3.3.257.1
Label 3.3.257.1-21.1-b
Conductor 21.1
Rank \( 0 \)

Related objects

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Base field 3.3.257.1

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

Elliptic curves in class 21.1-b over 3.3.257.1

Isogeny class 21.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
21.1-b1 \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 50 a^{2} + 10 a - 350\) , \( 432 a^{2} + 24 a - 2598\bigr] \)
21.1-b2 \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 10 a^{2} + 15 a - 85\) , \( -27 a^{2} - 50 a + 227\bigr] \)
21.1-b3 \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( -10 a^{2} - 15 a - 5\) , \( -65 a^{2} - 88 a + 51\bigr] \)
21.1-b4 \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( -5\) , \( -2 a^{2} - 3 a + 3\bigr] \)
21.1-b5 \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 0\) , \( 0\bigr] \)
21.1-b6 \( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( -230 a^{2} - 280 a + 340\) , \( -3614 a^{2} - 4360 a + 4812\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph