Elliptic curve isogeny class 4.1-c over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-4.1-c
• Conductor: 4.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4.1-c over \(\Q(\sqrt{57}) \)

Isogeny class 4.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
4.1-c1	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -2960 a - 9690\) , \( -168414 a - 551544\bigr] \)
4.1-c2	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 150 a + 495\) , \( -1331 a - 4361\bigr] \)
4.1-c3	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -149 a + 645\) , \( 1181 a - 5047\bigr] \)
4.1-c4	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 2961 a - 12650\) , \( 171374 a - 732608\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph