Elliptic curve isogeny class 128.7-f over number field 3.3.316.1

• Base field: 3.3.316.1
• Label: 3.3.316.1-128.7-f
• Conductor: 128.7
• 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

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

Isogeny graph

Elliptic curves in class 128.7-f over 3.3.316.1

Isogeny class 128.7-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
128.7-f1	\( \bigl[a^{2} - 3\) , \( -a\) , \( a^{2} + a - 2\) , \( -873 a^{2} + 2450 a - 955\) , \( -31027 a^{2} + 87293 a - 34213\bigr] \)
128.7-f2	\( \bigl[a^{2} - 3\) , \( -a\) , \( a^{2} + a - 2\) , \( -8 a^{2} + 20 a - 10\) , \( -71 a^{2} + 196 a - 78\bigr] \)
128.7-f3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -148 a^{2} + 585 a - 564\) , \( -3709 a^{2} + 10807 a - 4963\bigr] \)
128.7-f4	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 57 a^{2} - 25 a - 259\) , \( 357 a^{2} - 179 a - 1543\bigr] \)