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

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

Isogeny class 144.1-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
144.1-f1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -2847 a - 12409\) , \( 133896 a + 583639\bigr] \)
144.1-f2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -43527 a - 189729\) , \( 10154232 a + 44261271\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph