Elliptic curve isogeny class 16.1-a over number field 4.4.17725.1

• Base field: 4.4.17725.1
• Label: 4.4.17725.1-16.1-a
• Conductor: 16.1
• Rank: \( 1 \)

Base field 4.4.17725.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 12 x^{2} + 13 x + 41 \); class number \(1\).

Elliptic curves in class 16.1-a over 4.4.17725.1

Isogeny class 16.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{2} - 2 a - 6\) , \( a^{2} - a - 6\) , \( 2 a^{3} - 2 a^{2} - 10 a + 1\) , \( 10 a^{3} - 32 a^{2} - 37 a + 132\bigr] \)
16.1-a2	\( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{2} - 2 a - 6\) , \( a^{2} - a - 6\) , \( 152 a^{3} - 632 a^{2} - 350 a + 2591\) , \( 2636 a^{3} - 11350 a^{2} - 5341 a + 46488\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph