Properties

Base field 6.6.1541581.1
Label 6.6.1541581.1-25.1-c
Conductor 25.1
Rank \( 0 \)

Related objects

Learn more

Base field 6.6.1541581.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 6 x^{4} + 2 x^{3} + 9 x^{2} + x - 1 \); class number \(1\).

Elliptic curves in class 25.1-c over 6.6.1541581.1

Isogeny class 25.1-c contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
25.1-c1 \( \bigl[3 a^{5} - 5 a^{4} - 13 a^{3} + 12 a^{2} + 13 a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + 2 a + 2\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 6 a + 1\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 16 a^{2} + 5\) , \( 11 a^{5} - 24 a^{4} - 35 a^{3} + 59 a^{2} + 19 a - 2\bigr] \)
25.1-c2 \( \bigl[a^{5} - a^{4} - 6 a^{3} + 3 a^{2} + 9 a - 1\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 7 a^{2} - 9 a + 2\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 6 a + 1\) , \( -9 a^{5} + 14 a^{4} + 43 a^{3} - 36 a^{2} - 50 a + 10\) , \( -20 a^{5} + 40 a^{4} + 75 a^{3} - 104 a^{2} - 61 a + 17\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph