Elliptic curve isogeny class 128.3-b over number field 3.3.316.1

• Base field: 3.3.316.1
• Label: 3.3.316.1-128.3-b
• Conductor: 128.3
• Rank: \( 0 \)

Base field 3.3.316.1

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 128.3-b over 3.3.316.1

Isogeny class 128.3-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
128.3-b1	\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( 0\) , \( 8 a^{2} - 6 a - 54\) , \( -128 a^{2} - 94 a + 246\bigr] \)
128.3-b2	\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( 0\) , \( 8 a^{2} + 14 a - 14\) , \( 8 a^{2} + 18 a - 10\bigr] \)
128.3-b3	\( \bigl[a^{2} + a - 2\) , \( a + 1\) , \( 0\) , \( 224 a^{2} - 107 a - 934\) , \( 2719 a^{2} - 1426 a - 11531\bigr] \)
128.3-b4	\( \bigl[a^{2} + a - 2\) , \( -a^{2} + a + 3\) , \( 0\) , \( -2 a^{2} + 15 a - 2\) , \( -19 a^{2} + 62 a - 23\bigr] \)