Elliptic curve isogeny class 144.1-j over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-144.1-j
• Conductor: 144.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{19}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).

Elliptic curves in class 144.1-j over \(\Q(\sqrt{19}) \)

Isogeny class 144.1-j contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
144.1-j1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -141 a + 638\) , \( -1792 a + 7842\bigr] \)
144.1-j2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 150 a + 648\) , \( 2430 a + 10602\bigr] \)
144.1-j3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -45 a - 202\) , \( 84 a + 376\bigr] \)
144.1-j4	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 54 a - 212\) , \( -296 a + 1321\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph