Elliptic curve isogeny class 19.1-a over number field 6.6.1312625.1

• Base field: 6.6.1312625.1
• Label: 6.6.1312625.1-19.1-a
• Conductor: 19.1
• Rank: \( 1 \)

Base field 6.6.1312625.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 7 x^{4} + 7 x^{3} + 12 x^{2} - 12 x - 1 \); class number \(1\).

Elliptic curves in class 19.1-a over 6.6.1312625.1

Isogeny class 19.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
19.1-a1	\( \bigl[a^{2} - 3\) , \( -a^{3} + 2 a\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 8 a + 4\) , \( a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 7\) , \( a^{5} + 2 a^{4} - 10 a^{3} - 6 a^{2} + 19 a - 1\bigr] \)
19.1-a2	\( \bigl[a^{3} - 3 a + 1\) , \( a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 11 a - 1\) , \( a^{2} + a - 3\) , \( -3 a^{5} - a^{4} + 22 a^{3} - a^{2} - 40 a + 21\) , \( 9 a^{5} - 21 a^{4} - 31 a^{3} + 93 a^{2} - 27 a - 27\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph