Elliptic curve isogeny class 72.1-h over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-72.1-h
• Conductor: 72.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 72.1-h over \(\Q(\sqrt{19}) \)

Isogeny class 72.1-h contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
72.1-h1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 14692 a - 64033\) , \( 1661376 a - 7241757\bigr] \)
72.1-h2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 4522 a - 19703\) , \( -316646 a + 1380241\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph