Elliptic curve isogeny class 79.2-c over number field \(\Q(\zeta_{20})^+\)

• Base field: \(\Q(\zeta_{20})^+\)
• Label: 4.4.2000.1-79.2-c
• Conductor: 79.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 79.2-c over \(\Q(\zeta_{20})^+\)

Isogeny class 79.2-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
79.2-c1	\( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( -4 a^{3} + 12 a - 9\) , \( -a^{3} - 10 a^{2} - 4 a + 19\bigr] \)
79.2-c2	\( \bigl[a^{3} + a^{2} - 2 a - 3\) , \( 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a^{3} - 3 a + 1\) , \( a^{3} - 3 a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph