Elliptic curve isogeny class 9.2-a over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-9.2-a
• Conductor: 9.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 9.2-a over \(\Q(\sqrt{19}) \)

Isogeny class 9.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
9.2-a1	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 2 a + 32\) , \( 9 a + 29\bigr] \)
9.2-a2	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 87 a + 381\) , \( 349 a + 1521\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph