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

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-144.1-a
• 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-a over \(\Q(\sqrt{13}) \)

Isogeny class 144.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
144.1-a1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 16 a + 20\) , \( 16 a + 20\bigr] \)
144.1-a2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 9\) , \( 0\bigr] \)
144.1-a3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -16 a + 36\) , \( -16 a + 36\bigr] \)
144.1-a4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 49 a - 114\) , \( -237 a + 546\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph