Elliptic curve isogeny class 171.1-i over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-171.1-i
• Conductor: 171.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 171.1-i over \(\Q(\sqrt{19}) \)

Isogeny class 171.1-i contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
171.1-i1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 175 a - 862\) , \( -2828 a + 12735\bigr] \)
171.1-i2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \)
171.1-i3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \)
171.1-i4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \)
171.1-i5	\( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \)
171.1-i6	\( \bigl[1\) , \( 0\) , \( 1\) , \( -175 a - 862\) , \( 2828 a + 12735\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph