Elliptic curve isogeny class 13.4-a over number field 6.6.703493.1

• Base field: 6.6.703493.1
• Label: 6.6.703493.1-13.4-a
• Conductor: 13.4
• Rank: \( 1 \)

Base field 6.6.703493.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 5 x^{4} + 11 x^{3} + 2 x^{2} - 9 x + 1 \); class number \(1\).

Elliptic curves in class 13.4-a over 6.6.703493.1

Isogeny class 13.4-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
13.4-a1	\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 6 a^{2} + 14 a - 3\) , \( -a^{5} + a^{4} + 6 a^{3} - 6 a^{2} - 5 a + 4\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( a^{5} - 4 a^{3} + a^{2} - a + 5\) , \( a^{5} - 5 a^{3} + 5 a + 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph