Elliptic curve isogeny class 14.1-a over number field 5.5.138136.1

• Base field: 5.5.138136.1
• Label: 5.5.138136.1-14.1-a
• Conductor: 14.1
• Rank: \( 1 \)

Base field 5.5.138136.1

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

Elliptic curves in class 14.1-a over 5.5.138136.1

Isogeny class 14.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
14.1-a1	\( \bigl[2 a^{4} - 13 a^{2} - 4 a + 7\) , \( -4 a^{4} + a^{3} + 25 a^{2} + 7 a - 13\) , \( 1\) , \( -25 a^{4} + 8 a^{3} + 154 a^{2} + 25 a - 80\) , \( 28 a^{4} - 16 a^{3} - 175 a^{2} + 10 a + 121\bigr] \)
14.1-a2	\( \bigl[2 a^{4} - a^{3} - 12 a^{2} + 7\) , \( -a^{4} + a^{3} + 6 a^{2} - 3 a - 3\) , \( 1\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 13 a - 8\) , \( -a^{3} + 3 a^{2} + 8 a - 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph