Elliptic curve isogeny class 19.3-a over number field 3.3.761.1

• Base field: 3.3.761.1
• Label: 3.3.761.1-19.3-a
• Conductor: 19.3
• Rank: \( 1 \)

Base field 3.3.761.1

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

Elliptic curves in class 19.3-a over 3.3.761.1

Isogeny class 19.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
19.3-a1	\( \bigl[a^{2} - 4\) , \( -1\) , \( a + 1\) , \( -a^{2} + 2 a + 5\) , \( a + 1\bigr] \)
19.3-a2	\( \bigl[a^{2} - 4\) , \( -1\) , \( a + 1\) , \( -6 a^{2} + 7 a + 5\) , \( -41 a - 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph