Elliptic curve isogeny class 72.1-a over number field \(\Q(\zeta_{9})^+\)

• Base field: \(\Q(\zeta_{9})^+\)
• Label: 3.3.81.1-72.1-a
• Conductor: 72.1
• Rank: \( 0 \)

Base field \(\Q(\zeta_{9})^+\)

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

Elliptic curves in class 72.1-a over \(\Q(\zeta_{9})^+\)

Isogeny class 72.1-a contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
72.1-a1	\( \bigl[a^{2} + a - 2\) , \( 0\) , \( a\) , \( -675 a^{2} + 234 a + 1944\) , \( 1420 a^{2} - 493 a - 4089\bigr] \)
72.1-a2	\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( a\) , \( 7 a^{2} - 4 a - 23\) , \( 19 a^{2} - 7 a - 56\bigr] \)
72.1-a3	\( \bigl[a\) , \( a + 1\) , \( a^{2} - 1\) , \( 62084 a^{2} - 21557 a - 178770\) , \( -19632547 a^{2} + 6818300 a + 56529689\bigr] \)
72.1-a4	\( \bigl[1\) , \( -1\) , \( a^{2} - 2\) , \( 97935972 a^{2} - 34012315 a - 281996316\) , \( -605943656315 a^{2} + 210442015511 a + 1744745235998\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)

Isogeny graph