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

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-144.1-a
• 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-a over \(\Q(\sqrt{19}) \)

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

Curve label	Weierstrass Coefficients
144.1-a1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -142 a + 635\) , \( 1993 a - 8681\bigr] \)
144.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 149 a + 645\) , \( -1358 a - 5921\bigr] \)
144.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -46 a - 205\) , \( -447 a - 1950\bigr] \)
144.1-a4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 53 a - 215\) , \( 232 a - 1005\bigr] \)

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