Elliptic curve isogeny class 19.1-b over number field 3.3.1129.1

• Base field: 3.3.1129.1
• Label: 3.3.1129.1-19.1-b
• Conductor: 19.1
• 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 19.1-b over 3.3.1129.1

Isogeny class 19.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
19.1-b1	\( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - 5\) , \( -3 a^{2} - 10 a - 1\) , \( 11 a^{2} + 27 a + 4\bigr] \)
19.1-b2	\( \bigl[0\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -2 a^{2} + 4 a + 6\) , \( a^{2} - 3 a - 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph