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

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-432.1-g
• Conductor: 432.1
• Rank: \( 1 \)

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

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

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

Isogeny class 432.1-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
432.1-g1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -15 a + 45\) , \( 412 a - 1081\bigr] \)
432.1-g2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 14 a + 38\) , \( -70 a - 185\bigr] \)
432.1-g3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 5 a - 10\) , \( -5 a + 14\bigr] \)
432.1-g4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 25 a - 65\) , \( 110 a - 291\bigr] \)
432.1-g5	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 65 a - 175\) , \( -458 a + 1199\bigr] \)
432.1-g6	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 385 a - 1055\) , \( 6968 a - 18381\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph