Elliptic curve isogeny class 17.1-b over number field 3.3.1129.1

• Base field: 3.3.1129.1
• Label: 3.3.1129.1-17.1-b
• Conductor: 17.1
• Rank: \( 2 \)

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-b over 3.3.1129.1

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

Curve label	Weierstrass Coefficients
17.1-b1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -7 a - 3\) , \( 8 a^{2} - a - 2\bigr] \)
17.1-b2	\( \bigl[1\) , \( a^{2} - a - 5\) , \( a^{2} - a - 5\) , \( -2234 a^{2} + 5354 a + 2802\) , \( 127672 a^{2} - 306112 a - 159752\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph