Elliptic curve isogeny class 144.1-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-144.1-b
• Conductor: 144.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{13}) \)

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

Elliptic curves in class 144.1-b over \(\Q(\sqrt{13}) \)

Isogeny class 144.1-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
144.1-b1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 16 a - 44\) , \( -80 a + 120\bigr] \)
144.1-b2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 9 a - 18\) , \( -3 a + 18\bigr] \)
144.1-b3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -9 a - 9\) , \( 3 a + 15\bigr] \)
144.1-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 79 a - 193\) , \( 515 a - 1193\bigr] \)
144.1-b5	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 13\) , \( 8 a - 14\bigr] \)
144.1-b6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a - 9\) , \( -8 a - 6\bigr] \)
144.1-b7	\( \bigl[0\) , \( -1\) , \( 0\) , \( -16 a - 28\) , \( 80 a + 40\bigr] \)
144.1-b8	\( \bigl[0\) , \( -1\) , \( 0\) , \( -79 a - 114\) , \( -515 a - 678\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph