Elliptic curve isogeny class 16.3-e over number field 3.3.733.1

• Base field: 3.3.733.1
• Label: 3.3.733.1-16.3-e
• Conductor: 16.3
• Rank: \( 1 \)

Base field 3.3.733.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 8 \); class number \(1\).

Elliptic curves in class 16.3-e over 3.3.733.1

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

Curve label	Weierstrass Coefficients
16.3-e1	\( \bigl[a^{2} + a - 4\) , \( 1\) , \( a\) , \( -5 a^{2} + 26 a - 24\) , \( 29 a^{2} - 99 a + 76\bigr] \)
16.3-e2	\( \bigl[a\) , \( 1\) , \( a^{2} + a - 4\) , \( -41 a^{2} + 148 a - 116\) , \( 406 a^{2} - 1504 a + 1208\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph