Elliptic curve isogeny class 13.1-a over number field 3.3.229.1

• Base field: 3.3.229.1
• Label: 3.3.229.1-13.1-a
• Conductor: 13.1
• Rank: \( 0 \)

Base field 3.3.229.1

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

Elliptic curves in class 13.1-a over 3.3.229.1

Isogeny class 13.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
13.1-a1	\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( -2 a^{2} + 3 a + 1\) , \( 2 a^{2} - 3 a - 4\bigr] \)
13.1-a2	\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( -12 a^{2} + 23 a + 6\) , \( -40 a^{2} + 75 a + 19\bigr] \)
13.1-a3	\( \bigl[a\) , \( -a^{2} + a + 4\) , \( a\) , \( -7 a^{2} - 11 a + 2\) , \( -21 a^{2} - 44 a - 10\bigr] \)
13.1-a4	\( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -2 a^{2} + 7\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph