Elliptic curve isogeny class 57.1-a over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-57.1-a
• Conductor: 57.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 57.1-a over \(\Q(\sqrt{57}) \)

Isogeny class 57.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
57.1-a1	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -53035227 a - 173685972\) , \( 408531845304 a + 1337907974141\bigr] \)
57.1-a2	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 237573 a + 778038\) , \( 139619034 a + 457240781\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph