Elliptic curve isogeny class 432.1-j over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-432.1-j
• Conductor: 432.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 432.1-j over \(\Q(\sqrt{7}) \)

Isogeny class 432.1-j contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
432.1-j1	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -3 a\) , \( a + 5\bigr] \)
432.1-j2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 332 a - 874\) , \( 2132 a - 5639\bigr] \)
432.1-j3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 48 a - 126\) , \( 268 a - 709\bigr] \)
432.1-j4	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -660 a - 1746\) , \( 15039 a + 39789\bigr] \)