Properties

Base field 5.5.160801.1
Label 5.5.160801.1-23.1-a
Conductor 23.1
Rank \( 1 \)

Related objects

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Base field 5.5.160801.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 3 x - 1 \); class number \(1\).

Elliptic curves in class 23.1-a over 5.5.160801.1

Isogeny class 23.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
23.1-a1 \( \bigl[a^{2} + a - 1\) , \( 1\) , \( a^{4} - 5 a^{2} + 3\) , \( -8 a^{4} + 8 a^{3} + 44 a^{2} - 24 a - 31\) , \( 18 a^{4} - 10 a^{3} - 90 a^{2} + 41 a + 62\bigr] \)
23.1-a2 \( \bigl[a^{4} - 5 a^{2} + a + 3\) , \( a - 1\) , \( a^{4} - 4 a^{2} + a + 1\) , \( -3 a^{4} + 2 a^{3} + 14 a^{2} - 10 a - 11\) , \( 6 a^{4} - 6 a^{3} - 33 a^{2} + 20 a + 25\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph