Elliptic curve isogeny class 192.7-l over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.7-l
• Conductor: 192.7
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

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 192.7-l over \(\Q(\sqrt{57}) \)

Isogeny class 192.7-l contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
192.7-l1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 2 a + 3\) , \( a + 1\bigr] \)
192.7-l2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1150 a - 4916\) , \( 42711 a - 182586\bigr] \)
192.7-l3	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 18355 a - 78466\) , \( 2660510 a - 11373460\bigr] \)
192.7-l4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -67389 a - 220691\) , \( -18602828 a - 60922721\bigr] \)