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

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

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

Curve label	Weierstrass Coefficients
144.1-e1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 1038 a - 3070\) , \( 34376 a - 126732\bigr] \)
144.1-e2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -2 a - 510\) , \( 808 a - 1036\bigr] \)
144.1-e3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -2 a - 190\) , \( -216 a - 396\bigr] \)
144.1-e4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -1042 a - 3070\) , \( 30216 a + 114420\bigr] \)

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