Elliptic curve isogeny class 16.1-a over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-16.1-a
• Conductor: 16.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 16.1-a over \(\Q(\sqrt{57}) \)

Isogeny class 16.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 5\) , \( 133 a - 574\bigr] \)
16.1-a2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 5\) , \( -133 a - 436\bigr] \)
16.1-a3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 201 a - 850\) , \( 3094 a - 13232\bigr] \)
16.1-a4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -199 a - 650\) , \( -3294 a - 10788\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph