Elliptic curve isogeny class 175.4-a over number field \(\Q(\sqrt{-19}) \)

• Base field: \(\Q(\sqrt{-19}) \)
• Label: 2.0.19.1-175.4-a
• Conductor: 175.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 175.4-a over \(\Q(\sqrt{-19}) \)

Isogeny class 175.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
175.4-a1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a - 3\) , \( -2\bigr] \)
175.4-a2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -6 a - 3\) , \( 12 a - 7\bigr] \)
175.4-a3	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a + 2\) , \( -a + 1\bigr] \)
175.4-a4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 4 a - 83\) , \( 32 a - 269\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph