Elliptic curve isogeny class 17.1-a over number field 3.3.148.1

• Base field: 3.3.148.1
• Label: 3.3.148.1-17.1-a
• Conductor: 17.1
• 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 17.1-a over 3.3.148.1

Isogeny class 17.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
17.1-a1	\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( 238 a^{2} - 154 a - 789\) , \( -2388 a^{2} + 1668 a + 7624\bigr] \)
17.1-a2	\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( 28 a^{2} - 24 a - 99\) , \( 108 a^{2} - 86 a - 366\bigr] \)
17.1-a3	\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( 13 a^{2} - 9 a - 44\) , \( -22 a^{2} + 15 a + 69\bigr] \)
17.1-a4	\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a\) , \( -2 a^{2} + a + 6\) , \( -3 a^{2} + 2 a + 9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph