Properties

Base field 4.4.16357.1
Label 4.4.16357.1-15.2-b
Conductor 15.2
Rank \( 1 \)

Related objects

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Base field 4.4.16357.1

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

Elliptic curves in class 15.2-b over 4.4.16357.1

Isogeny class 15.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
15.2-b1 \( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a^{2} - a + 3\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 4 a^{3} - 2 a^{2} - 26 a - 9\) , \( 22 a^{3} + 6 a^{2} - 137 a - 68\bigr] \)
15.2-b2 \( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a^{2} - a + 3\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -a^{3} - 2 a^{2} + 4 a + 6\) , \( -a^{3} - a^{2} + 5 a + 4\bigr] \)
15.2-b3 \( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -14 a^{3} + 13 a^{2} + 77 a - 66\) , \( 74 a^{3} - 42 a^{2} - 425 a + 164\bigr] \)
15.2-b4 \( \bigl[a^{3} - 5 a\) , \( -a^{3} - a^{2} + 5 a + 5\) , \( 0\) , \( -3 a^{3} - a^{2} + 15 a + 12\) , \( -3 a^{3} + 2 a^{2} + 14 a + 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph