Elliptic curve isogeny class 192.6-d over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.6-d
• Conductor: 192.6
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 192.6-d over \(\Q(\sqrt{57}) \)

Isogeny class 192.6-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
192.6-d1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 2 a + 1\) , \( 9 a + 34\bigr] \)
192.6-d2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -71829 a - 235234\) , \( -8626826 a - 28252141\bigr] \)
192.6-d3	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 142 a - 579\) , \( -1418 a + 6107\bigr] \)
192.6-d4	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 737 a - 3124\) , \( 19386 a - 82833\bigr] \)