Elliptic curve isogeny class 6.2-a over number field 4.4.17428.1

• Base field: 4.4.17428.1
• Label: 4.4.17428.1-6.2-a
• Conductor: 6.2
• Rank: \( 1 \)

Base field 4.4.17428.1

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

Elliptic curves in class 6.2-a over 4.4.17428.1

Isogeny class 6.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
6.2-a1	\( \bigl[a^{3} - 4 a\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 9 a^{3} + 12 a^{2} - 20 a - 18\) , \( 69 a^{3} + 96 a^{2} - 188 a - 174\bigr] \)
6.2-a2	\( \bigl[a\) , \( a^{3} - 4 a - 2\) , \( a^{3} - 4 a - 1\) , \( -31 a^{3} - 42 a^{2} + 88 a + 81\) , \( 129 a^{3} + 176 a^{2} - 357 a - 328\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph