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

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-144.1-b
• Conductor: 144.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
144.1-b1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 1042 a - 3070\) , \( -30216 a + 114420\bigr] \)
144.1-b2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2 a - 510\) , \( -808 a - 1036\bigr] \)
144.1-b3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2 a - 190\) , \( 216 a - 396\bigr] \)
144.1-b4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -1038 a - 3070\) , \( -34376 a - 126732\bigr] \)

Rank

Rank: \( 1 \)

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