Properties

Base field 4.4.9909.1
Label 4.4.9909.1-13.1-a
Conductor 13.1
Rank \( 1 \)

Related objects

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Base field 4.4.9909.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} - 3 x + 3 \); class number \(1\).

Elliptic curves in class 13.1-a over 4.4.9909.1

Isogeny class 13.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
13.1-a1 \( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 5 a\) , \( 0\) , \( -17 a^{3} - 3 a^{2} + 34 a - 30\) , \( 45 a^{3} + 106 a^{2} + 25 a - 23\bigr] \)
13.1-a2 \( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 5 a\) , \( 0\) , \( -2 a^{3} + 2 a^{2} + 9 a - 5\) , \( -14 a^{3} + 17 a^{2} + 64 a - 35\bigr] \)
13.1-a3 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a\) , \( 0\) , \( 21 a^{3} + 8 a^{2} - 26 a - 9\) , \( 562 a^{3} + 1305 a^{2} + 277 a - 581\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph