Elliptic curve isogeny class 27.1-a over number field 6.6.1397493.1

• Base field: 6.6.1397493.1
• Label: 6.6.1397493.1-27.1-a
• Conductor: 27.1
• Rank: \( 0 \)

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-a over 6.6.1397493.1

Isogeny class 27.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
27.1-a1	\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 1\) , \( a^{5} - 4 a^{4} + a^{3} + 7 a^{2} - 3 a + 3\) , \( a^{4} - 3 a^{3} + 6 a - 3\) , \( 3 a^{5} - 14 a^{4} + 11 a^{3} + 15 a^{2} - 8 a - 2\) , \( 12 a^{5} - 56 a^{4} + 50 a^{3} + 62 a^{2} - 76 a + 19\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph