Elliptic curve isogeny class 71.2-e over number field 4.4.6125.1

• Base field: 4.4.6125.1
• Label: 4.4.6125.1-71.2-e
• Conductor: 71.2
• Rank: \( 1 \)

Base field 4.4.6125.1

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

Elliptic curves in class 71.2-e over 4.4.6125.1

Isogeny class 71.2-e contains only one elliptic curve.

Curve label	Weierstrass Coefficients
71.2-e1	\( \bigl[a + 1\) , \( -a - 1\) , \( 2 a^{3} + 3 a^{2} - 12 a - 11\) , \( -15 a^{3} - 20 a^{2} + 86 a + 68\) , \( -25 a^{3} - 34 a^{2} + 145 a + 117\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph