Elliptic curve isogeny class 19.1-a over number field 3.3.148.1

• Base field: 3.3.148.1
• Label: 3.3.148.1-19.1-a
• Conductor: 19.1
• Rank: \( 0 \)

Base field 3.3.148.1

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

Elliptic curves in class 19.1-a over 3.3.148.1

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

Curve label	Weierstrass Coefficients
19.1-a1	\( \bigl[a^{2} - a - 2\) , \( -1\) , \( a\) , \( -10233 a^{2} - 11974 a + 4716\) , \( 1041051 a^{2} + 1218120 a - 479728\bigr] \)
19.1-a2	\( \bigl[a^{2} - a - 2\) , \( -1\) , \( a\) , \( -24578 a^{2} - 28759 a + 11326\) , \( -2418130 a^{2} - 2829421 a + 1114301\bigr] \)
19.1-a3	\( \bigl[0\) , \( -a^{2} + 2\) , \( a^{2} - a - 1\) , \( 20 a^{2} - 9 a - 70\) , \( 81 a^{2} - 52 a - 273\bigr] \)
19.1-a4	\( \bigl[0\) , \( -a^{2} + 2\) , \( a^{2} - a - 1\) , \( a\) , \( -1\bigr] \)

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