Properties

Base field 6.6.1241125.1
Label 6.6.1241125.1-45.1-e
Conductor 45.1
Rank \( 1 \)

Related objects

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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-e over 6.6.1241125.1

Isogeny class 45.1-e contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
45.1-e1 \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - 2 a^{2} - 23 a - 6\) , \( -a^{4} + 5 a^{2} + 2 a - 3\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( 43 a^{5} - 27 a^{4} - 294 a^{3} + 95 a^{2} + 461 a + 29\) , \( 159 a^{5} - 52 a^{4} - 1092 a^{3} + 30 a^{2} + 1716 a + 593\bigr] \)
45.1-e2 \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - 2 a^{2} - 23 a - 6\) , \( -a^{4} + 5 a^{2} + 2 a - 3\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( 43 a^{5} - 22 a^{4} - 294 a^{3} + 60 a^{2} + 461 a + 89\) , \( -176 a^{5} + 79 a^{4} + 1193 a^{3} - 187 a^{2} - 1836 a - 391\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph