Elliptic curve isogeny class 6272.2-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-6272.2-d
• Conductor: 6272.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 6272.2-d over \(\Q(\sqrt{-7}) \)

Isogeny class 6272.2-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
6272.2-d1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -746 a + 896\) , \( 424 a - 14864\bigr] \)
6272.2-d2	\( \bigl[a\) , \( -a\) , \( a\) , \( 66 a - 195\) , \( -471 a + 1026\bigr] \)
6272.2-d3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -46 a + 56\) , \( 4 a - 248\bigr] \)
6272.2-d4	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 18 a - 24\) , \( -92 a + 24\bigr] \)
6272.2-d5	\( \bigl[a\) , \( 0\) , \( 0\) , \( -39 a - 135\) , \( 23 a + 957\bigr] \)
6272.2-d6	\( \bigl[a\) , \( 0\) , \( 0\) , \( 31 a + 5\) , \( 37 a + 89\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph