Elliptic curve isogeny class 64.1-a over number field 6.6.300125.1

• Base field: 6.6.300125.1
• Label: 6.6.300125.1-64.1-a
• Conductor: 64.1
• Rank: \( 0 \)

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 64.1-a over 6.6.300125.1

Isogeny class 64.1-a contains 2 curves linked by isogenies of degree 13.

Curve label	Weierstrass Coefficients
64.1-a1	\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 9 a - 2\) , \( -3 a^{5} + a^{4} + 21 a^{3} + 8 a^{2} - 10 a - 1\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 29 a - 6\) , \( 10524 a^{5} - 2534 a^{4} - 75422 a^{3} - 36441 a^{2} + 45216 a + 13058\) , \( 342107 a^{5} - 79925 a^{4} - 2453847 a^{3} - 1199258 a^{2} + 1465409 a + 437699\bigr] \)
64.1-a2	\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 9 a - 2\) , \( -3 a^{5} + a^{4} + 21 a^{3} + 8 a^{2} - 10 a - 1\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 29 a - 6\) , \( -6 a^{5} + a^{4} + 43 a^{3} + 24 a^{2} - 24 a - 7\) , \( -10 a^{5} + 2 a^{4} + 72 a^{3} + 37 a^{2} - 42 a - 14\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph