Elliptic curve isogeny class 19.1-a over number field 3.3.257.1

• Base field: 3.3.257.1
• Label: 3.3.257.1-19.1-a
• Conductor: 19.1
• Rank: \( 0 \)

Base field 3.3.257.1

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

Elliptic curves in class 19.1-a over 3.3.257.1

Isogeny class 19.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
19.1-a1	\( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( 22 a^{2} - a - 116\) , \( 36 a^{2} - 32 a - 143\bigr] \)
19.1-a2	\( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( 22 a^{2} - 6 a - 91\) , \( 79 a^{2} - 21 a - 332\bigr] \)
19.1-a3	\( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( 2 a^{2} - a - 6\) , \( 2 a^{2} - 7\bigr] \)
19.1-a4	\( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a^{2} - 2\) , \( -8 a^{2} - a + 29\) , \( -3 a^{2} - 9 a - 5\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph