Elliptic curve isogeny class 17.1-a over number field 3.3.1129.1

• Base field: 3.3.1129.1
• Label: 3.3.1129.1-17.1-a
• Conductor: 17.1
• Rank: \( 1 \)

Base field 3.3.1129.1

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

Elliptic curves in class 17.1-a over 3.3.1129.1

Isogeny class 17.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
17.1-a1	\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 4\) , \( a^{2} - 4\) , \( 4 a^{2} - 14 a + 2\) , \( -47 a^{2} + 109 a + 66\bigr] \)
17.1-a2	\( \bigl[a\) , \( a - 1\) , \( a^{2} - a - 4\) , \( -11316 a^{2} + 27133 a + 14159\) , \( -1478065 a^{2} + 3543901 a + 1849381\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph