Elliptic curve isogeny class 100.1-b over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-100.1-b
• Conductor: 100.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 100.1-b over \(\Q(\sqrt{57}) \)

Isogeny class 100.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-b1	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 102 a - 433\) , \( 1404 a - 6003\bigr] \)
100.1-b2	\( \bigl[1\) , \( a\) , \( 1\) , \( 78 a + 258\) , \( -79 a - 260\bigr] \)
100.1-b3	\( \bigl[1\) , \( a\) , \( 1\) , \( -322 a - 1052\) , \( -2087 a - 6836\bigr] \)
100.1-b4	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 1702 a - 7273\) , \( 76860 a - 328571\bigr] \)

Rank

Rank: \( 1 \)

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