Properties

Base field 6.6.1387029.1
Label 6.6.1387029.1-49.1-d
Conductor 49.1
Rank \( 0 \)

Related objects

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Base field 6.6.1387029.1

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

Elliptic curves in class 49.1-d over 6.6.1387029.1

Isogeny class 49.1-d contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
49.1-d1 \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 2\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 15 a^{2} + 5 a - 4\) , \( a^{3} - 4 a\) , \( 14 a^{5} - 35 a^{4} - 45 a^{3} + 102 a^{2} + 27 a - 41\) , \( 129 a^{5} - 326 a^{4} - 365 a^{3} + 977 a^{2} + 170 a - 433\bigr] \)
49.1-d2 \( \bigl[-a^{5} + 3 a^{4} + 3 a^{3} - 8 a^{2} - 3 a + 3\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + a - 5\) , \( -2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 4 a + 4\) , \( -7 a^{5} + 34 a^{4} + 15 a^{3} - 106 a^{2} - 8 a + 46\) , \( -131 a^{5} + 406 a^{4} + 349 a^{3} - 1239 a^{2} - 161 a + 549\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph