Properties

Base field 6.6.1397493.1
Label 6.6.1397493.1-27.1-m
Conductor 27.1
Rank \( 0 \)

Related objects

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Base field 6.6.1397493.1

Generator \(a\), with minimal polynomial \( x^{6} - 3 x^{5} - 3 x^{4} + 10 x^{3} + 3 x^{2} - 6 x + 1 \); class number \(1\).

Elliptic curves in class 27.1-m over 6.6.1397493.1

Isogeny class 27.1-m contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
27.1-m1 \( \bigl[a^{4} - 3 a^{3} + 6 a - 3\) , \( a + 1\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 4\) , \( 72 a^{5} - 207 a^{4} - 214 a^{3} + 627 a^{2} + 284 a - 320\) , \( 454 a^{5} - 1296 a^{4} - 1463 a^{3} + 4088 a^{2} + 1968 a - 2141\bigr] \)
27.1-m2 \( \bigl[a^{4} - 3 a^{3} + 6 a - 3\) , \( a + 1\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 4\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 9 a - 5\) , \( 3 a^{5} - 3 a^{4} - 9 a^{3} + 5 a^{2} + 3 a - 5\bigr] \)
27.1-m3 \( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 3 a - 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 6 a^{2} + 3 a\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 9 a^{2} + 10 a - 5\) , \( -62 a^{5} + 238 a^{4} - 48 a^{3} - 493 a^{2} + 272 a - 34\) , \( 422 a^{5} - 1710 a^{4} + 611 a^{3} + 3428 a^{2} - 2482 a + 353\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph