Elliptic curve isogeny class 76.1-j over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-76.1-j
• Conductor: 76.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 76.1-j over \(\Q(\sqrt{57}) \)

Isogeny class 76.1-j contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
76.1-j1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -16\) , \( 22\bigr] \)
76.1-j2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -86\) , \( -2456\bigr] \)
76.1-j3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 9\) , \( 90\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph