Elliptic curve isogeny class 20.2-a over number field \(\Q(\sqrt{-19}) \)

• Base field: \(\Q(\sqrt{-19}) \)
• Label: 2.0.19.1-20.2-a
• Conductor: 20.2
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - x + 5 \); class number \(1\).

Elliptic curves in class 20.2-a over \(\Q(\sqrt{-19}) \)

Isogeny class 20.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
20.2-a1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( 2 a - 26\bigr] \)
20.2-a2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 14 a - 46\) , \( 54 a - 114\bigr] \)
20.2-a3	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph