Elliptic curve isogeny class 20.1-a over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-20.1-a
• Conductor: 20.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 20.1-a over \(\Q(\sqrt{19}) \)

Isogeny class 20.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
20.1-a1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -10255 a - 44704\) , \( -1216748 a - 5303685\bigr] \)
20.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -85 a - 374\) , \( -2930 a - 12775\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph