Elliptic curve isogeny class 14.3-a over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-14.3-a
• Conductor: 14.3
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 14.3-a over \(\Q(\sqrt{57}) \)

Isogeny class 14.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
14.3-a1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -a - 5\) , \( -a - 5\bigr] \)
14.3-a2	\( \bigl[a\) , \( a\) , \( a + 1\) , \( 14101 a + 46176\) , \( -608844 a - 1993915\bigr] \)