Elliptic curve isogeny class 171.1-h over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-171.1-h
• Conductor: 171.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Elliptic curves in class 171.1-h over \(\Q(\sqrt{57}) \)

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

Curve label	Weierstrass Coefficients
171.1-h1	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -1018 a + 4355\) , \( -104632 a + 447292\bigr] \)
171.1-h2	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 9960 a + 32625\) , \( 2264742 a + 7416846\bigr] \)
171.1-h3	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 182 a - 775\) , \( 2528 a - 10808\bigr] \)
171.1-h4	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 782 a - 3340\) , \( -19744 a + 84403\bigr] \)
171.1-h5	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -6 a - 12\) , \( 18 a + 63\bigr] \)
171.1-h6	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 12182 a - 52075\) , \( -1403704 a + 6000718\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph