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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-171.1-c
• Conductor: 171.1
• Rank: \( 1 \)

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

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

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

Isogeny class 171.1-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
171.1-c1	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -92319 a - 302343\) , \( -29828922 a - 97687237\bigr] \)
171.1-c2	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -1119 a - 3663\) , \( -44142 a - 144562\bigr] \)
171.1-c3	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 81 a + 267\) , \( 108 a + 353\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph