Elliptic Curve Isogeny Class 71.4-a over Number Field 6.6.300125.1

• Base field: 6.6.300125.1
• Label: 6.6.300125.1-71.4-a
• Conductor: 71.4
• Rank: not recorded

Base field 6.6.300125.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 7 x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 71.4-a over 6.6.300125.1

Isogeny class 71.4-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
71.4-a1	\( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 19 a - 6\) , \( 11 a^{5} - 3 a^{4} - 79 a^{3} - 36 a^{2} + 52 a + 17\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 27 a - 8\) , \( -74 a^{5} + 22 a^{4} + 533 a^{3} + 231 a^{2} - 348 a - 101\) , \( -794 a^{5} + 224 a^{4} + 5719 a^{3} + 2523 a^{2} - 3738 a - 1101\bigr] \)
71.4-a2	\( \bigl[a\) , \( -a^{5} + a^{4} + 7 a^{3} - 2 a^{2} - 7 a + 3\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 29 a - 10\) , \( 61 a^{5} - 13 a^{4} - 437 a^{3} - 222 a^{2} + 251 a + 75\) , \( 5699 a^{5} - 1304 a^{4} - 40900 a^{3} - 20142 a^{2} + 24368 a + 7391\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph