Elliptic curve isogeny class 71.1-g over number field 4.4.6125.1

• Base field: 4.4.6125.1
• Label: 4.4.6125.1-71.1-g
• Conductor: 71.1
• 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 71.1-g over 4.4.6125.1

Isogeny class 71.1-g contains only one elliptic curve.

Curve label	Weierstrass Coefficients
71.1-g1	\( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( a^{2} + a - 5\) , \( 2 a^{3} + 3 a^{2} - 12 a - 12\) , \( -a^{3} - 3 a^{2} + 6 a + 15\) , \( 44 a^{3} + 61 a^{2} - 254 a - 211\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph