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

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.6-t
• 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

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

Isogeny graph

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

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

Curve label	Weierstrass Coefficients
192.6-t1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 49010 a + 160505\) , \( 23618409 a + 77348334\bigr] \)
192.6-t2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -27995 a - 91680\) , \( 4133278 a + 13536143\bigr] \)
192.6-t3	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -46 a - 145\) , \( -336 a - 1098\bigr] \)
192.6-t4	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 162 a - 702\) , \( -9840 a + 42060\bigr] \)