Properties

Base field 6.6.1241125.1
Label 6.6.1241125.1-45.1-b
Conductor 45.1
Rank not recorded

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Base field 6.6.1241125.1

Generator \(a\), with minimal polynomial \( x^{6} - 7 x^{4} - 2 x^{3} + 11 x^{2} + 7 x + 1 \); class number \(1\).

Elliptic curves in class 45.1-b over 6.6.1241125.1

Isogeny class 45.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
45.1-b1 \( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 13\) , \( a^{5} - 7 a^{3} - a^{2} + 11 a + 4\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( 686 a^{5} - 226 a^{4} - 4542 a^{3} + 352 a^{2} + 6572 a + 1376\) , \( 8264 a^{5} - 4931 a^{4} - 57506 a^{3} + 14498 a^{2} + 94248 a + 19342\bigr] \)
45.1-b2 \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 10\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 12\) , \( 132 a^{5} - 252 a^{4} - 589 a^{3} + 1066 a^{2} + 151 a - 199\) , \( -9857 a^{5} + 12020 a^{4} + 53933 a^{3} - 45477 a^{2} - 50903 a - 9271\bigr] \)
45.1-b3 \( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 29 a - 11\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} + 5 a^{2} + 32 a + 11\) , \( -a^{5} + a^{4} + 7 a^{3} - 3 a^{2} - 11 a - 3\) , \( 84 a^{5} - 45 a^{4} - 565 a^{3} + 105 a^{2} + 891 a + 212\) , \( 298 a^{5} - 153 a^{4} - 1998 a^{3} + 365 a^{2} + 3103 a + 667\bigr] \)
45.1-b4 \( \bigl[-3 a^{5} + a^{4} + 20 a^{3} - 29 a - 11\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} + 5 a^{2} + 32 a + 11\) , \( -a^{5} + a^{4} + 7 a^{3} - 3 a^{2} - 11 a - 3\) , \( 19 a^{5} - 10 a^{4} - 135 a^{3} + 20 a^{2} + 231 a + 82\) , \( 21 a^{5} - 11 a^{4} - 150 a^{3} + 20 a^{2} + 261 a + 96\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph