Elliptic curve isogeny class 64.4-f over number field 3.3.733.1

• Base field: 3.3.733.1
• Label: 3.3.733.1-64.4-f
• Conductor: 64.4
• Rank: \( 0 \)

Base field 3.3.733.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 8 \); class number \(1\).

Elliptic curves in class 64.4-f over 3.3.733.1

Isogeny class 64.4-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
64.4-f1	\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 6\) , \( a^{2} + a - 4\) , \( 8 a^{2} - 38 a + 40\) , \( 46 a^{2} - 177 a + 148\bigr] \)
64.4-f2	\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 4\) , \( a^{2} + a - 4\) , \( -19 a^{2} + 65 a - 48\) , \( 90 a^{2} - 333 a + 268\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph