Elliptic curve isogeny class 16.1-a over number field 4.4.12725.1

• Base field: 4.4.12725.1
• Label: 4.4.12725.1-16.1-a
• Number of curves: 1
• Conductor: 16.1
• Rank: \( 2 \)

Base field 4.4.12725.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 10 x^{2} + 11 x + 29 \); class number \(1\).

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 16.1-a over 4.4.12725.1

Isogeny class 16.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 5 a\) , \( a^{2} - a - 6\) , \( -273 a^{3} + 984 a^{2} + 1094 a - 4719\) , \( 5413 a^{3} - 19757 a^{2} - 21474 a + 94946\bigr] \)