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

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

Isogeny class 171.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
171.1-a1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 526841 a - 2252236\) , \( 404829173 a - 1730611020\bigr] \)
171.1-a2	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -2359 a + 10094\) , \( 136703 a - 584400\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph