Properties

Base field 4.4.16448.1
Label 4.4.16448.1-16.1-c
Conductor 16.1
Rank \( 1 \)

Related objects

Learn more about

Base field 4.4.16448.1

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

Elliptic curves in class 16.1-c over 4.4.16448.1

Isogeny class 16.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
16.1-c1 \( \bigl[0\) , \( -a^{3} + 3 a^{2} + 4 a - 2\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( 4 a^{3} - 14 a^{2} - 6 a + 7\) , \( -6 a^{3} + 17 a^{2} + 7 a - 10\bigr] \)
16.1-c2 \( \bigl[a\) , \( a^{3} - 3 a^{2} - 4 a + 2\) , \( 0\) , \( 182 a^{3} - 266 a^{2} - 1235 a - 667\) , \( -2651 a^{3} + 3863 a^{2} + 18003 a + 9771\bigr] \)
16.1-c3 \( \bigl[a^{3} - 3 a^{2} - 3 a + 2\) , \( -a^{2} + 2 a + 3\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( -4 a^{3} + 11 a^{2} + 21 a - 26\) , \( -20 a^{3} + 51 a^{2} + 92 a - 63\bigr] \)
16.1-c4 \( \bigl[a^{3} - 3 a^{2} - 2 a + 2\) , \( -1\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( a^{3} - 4 a^{2}\) , \( a^{3} - 4 a^{2} + 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph