Elliptic curve isogeny class 16.3-b over number field 4.4.9248.1

• Base field: 4.4.9248.1
• Label: 4.4.9248.1-16.3-b
• Conductor: 16.3
• Rank: \( 1 \)

Base field 4.4.9248.1

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

Elliptic curves in class 16.3-b over 4.4.9248.1

Isogeny class 16.3-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
16.3-b1	\( \bigl[a^{2} + a - 2\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a + 1\) , \( 47 a^{3} + 28 a^{2} - 216 a - 130\) , \( -444 a^{3} - 296 a^{2} + 2025 a + 1349\bigr] \)
16.3-b2	\( \bigl[a^{2} + a - 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 4 a + 1\) , \( -3 a^{3} - 7 a^{2} + 2 a + 7\) , \( -5 a^{3} - 9 a^{2} + 5 a + 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph