Elliptic curve isogeny class 175.3-a over number field \(\Q(\sqrt{-19}) \)

• Base field: \(\Q(\sqrt{-19}) \)
• Label: 2.0.19.1-175.3-a
• Conductor: 175.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 175.3-a over \(\Q(\sqrt{-19}) \)

Isogeny class 175.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
175.3-a1	\( \bigl[a\) , \( 0\) , \( a\) , \( -a - 2\) , \( -a - 1\bigr] \)
175.3-a2	\( \bigl[a\) , \( 0\) , \( a\) , \( -a + 3\) , \( 1\bigr] \)
175.3-a3	\( \bigl[a\) , \( 0\) , \( a\) , \( 4 a - 7\) , \( -13 a + 6\bigr] \)
175.3-a4	\( \bigl[a\) , \( 0\) , \( a\) , \( -6 a - 77\) , \( -33 a - 236\bigr] \)

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