Elliptic curve isogeny class 16.3-a over number field 3.3.733.1

• Base field: 3.3.733.1
• Label: 3.3.733.1-16.3-a
• Conductor: 16.3
• Rank: \( 0 \)

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-a over 3.3.733.1

Isogeny class 16.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
16.3-a1	\( \bigl[0\) , \( a + 1\) , \( a^{2} - 4\) , \( -8 a^{2} - 16 a + 16\) , \( -55 a^{2} - 79 a + 184\bigr] \)
16.3-a2	\( \bigl[0\) , \( a + 1\) , \( a^{2} - 4\) , \( -938 a^{2} - 1396 a + 3056\) , \( -29345 a^{2} - 44566 a + 93184\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph