Elliptic curve isogeny class 16.2-b over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-16.2-b
• Conductor: 16.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 16.2-b over \(\Q(\sqrt{57}) \)

Isogeny class 16.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
16.2-b1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 27 a - 113\) , \( 195 a - 833\bigr] \)
16.2-b2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -84 a - 276\) , \( -1037 a - 3397\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph