Elliptic curve isogeny class 64.1-b over number field \(\Q(\zeta_{13})^+\)

• Base field: \(\Q(\zeta_{13})^+\)
• Label: 6.6.371293.1-64.1-b
• Conductor: 64.1
• Rank: \( 1 \)

Base field \(\Q(\zeta_{13})^+\)

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 5 x^{4} + 4 x^{3} + 6 x^{2} - 3 x - 1 \); class number \(1\).

Elliptic curves in class 64.1-b over \(\Q(\zeta_{13})^+\)

Isogeny class 64.1-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
64.1-b1	\( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a + 1\) , \( 1801 a^{5} + 962 a^{4} - 7561 a^{3} - 4471 a^{2} + 4023 a + 1051\) , \( 70970 a^{5} + 36003 a^{4} - 301077 a^{3} - 170680 a^{2} + 170108 a + 46396\bigr] \)
64.1-b2	\( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a + 1\) , \( a^{5} + 2 a^{4} - a^{3} - a^{2} + 3 a + 1\) , \( -20 a^{5} - 7 a^{4} + 93 a^{3} + 50 a^{2} - 52 a - 14\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph