Elliptic curve isogeny class 79.3-a over number field \(\Q(\zeta_{20})^+\)

• Base field: \(\Q(\zeta_{20})^+\)
• Label: 4.4.2000.1-79.3-a
• Conductor: 79.3
• Rank: \( 0 \)

Base field \(\Q(\zeta_{20})^+\)

Generator \(a\), with minimal polynomial \( x^{4} - 5 x^{2} + 5 \); class number \(1\).

Elliptic curves in class 79.3-a over \(\Q(\zeta_{20})^+\)

Isogeny class 79.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
79.3-a1	\( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 2\) , \( -5 a^{3} - 6 a^{2} + 14 a + 15\) , \( 3 a^{3} + 2 a^{2} - 16 a - 17\bigr] \)
79.3-a2	\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} - a + 3\) , \( a^{3} - 2 a\) , \( -a^{3} + a^{2} + a - 3\) , \( 5 a^{3} - 9 a^{2} - 8 a + 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph