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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-171.1-j
• 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-j over \(\Q(\sqrt{57}) \)

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

Curve label	Weierstrass Coefficients
171.1-j1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 92321 a - 394663\) , \( 29736602 a - 127121496\bigr] \)
171.1-j2	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 1121 a - 4783\) , \( 43022 a - 183921\bigr] \)
171.1-j3	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -79 a + 347\) , \( -28 a + 114\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph