Elliptic curve isogeny class 13.1-a over number field 3.3.733.1

• Base field: 3.3.733.1
• Label: 3.3.733.1-13.1-a
• Conductor: 13.1
• 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 13.1-a over 3.3.733.1

Isogeny class 13.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
13.1-a1	\( \bigl[0\) , \( a^{2} - 5\) , \( a^{2} - 5\) , \( -a - 1\) , \( -5 a^{2} - 5 a + 22\bigr] \)
13.1-a2	\( \bigl[0\) , \( a^{2} - 5\) , \( a^{2} - 5\) , \( -90 a^{2} - 151 a + 249\) , \( -1051 a^{2} - 1622 a + 3267\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph