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

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

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

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

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

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

Curve label	Weierstrass Coefficients
432.1-c1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -17 a + 40\) , \( -428 a + 1123\bigr] \)
432.1-c2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a + 38\) , \( 70 a + 185\bigr] \)
432.1-c3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 3 a - 15\) , \( 9 a - 27\bigr] \)
432.1-c4	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 23 a - 70\) , \( -86 a + 223\bigr] \)
432.1-c5	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 63 a - 180\) , \( 522 a - 1377\bigr] \)
432.1-c6	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 383 a - 1060\) , \( -6584 a + 17323\bigr] \)

Rank

Rank: \( 0 \)

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