Elliptic curve isogeny class 144.3-c over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-144.3-c
• Conductor: 144.3
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 144.3-c over \(\Q(\sqrt{13}) \)

Isogeny class 144.3-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
144.3-c1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -10 a - 11\) , \( 2 a + 2\bigr] \)
144.3-c2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 121 a - 283\) , \( -1089 a + 2502\bigr] \)
144.3-c3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 46 a - 109\) , \( -191 a + 441\bigr] \)
144.3-c4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 6 a - 18\) , \( -23 a + 47\bigr] \)