Elliptic curve isogeny class 96.3-j over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-96.3-j
• Conductor: 96.3
• 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 96.3-j over \(\Q(\sqrt{57}) \)

Isogeny class 96.3-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
96.3-j1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 15 a - 39\) , \( -31 a + 171\bigr] \)
96.3-j2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 5 a + 1\) , \( 5 a + 7\bigr] \)
96.3-j3	\( \bigl[a\) , \( 0\) , \( a\) , \( -830 a + 3546\) , \( 11647 a - 49791\bigr] \)
96.3-j4	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -272 a - 888\) , \( 4766 a + 15610\bigr] \)