Elliptic curve isogeny class 6272.7-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-6272.7-d
• Conductor: 6272.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 6272.7-d over \(\Q(\sqrt{-7}) \)

Isogeny class 6272.7-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
6272.7-d1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 746 a + 150\) , \( -424 a - 14440\bigr] \)
6272.7-d2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -68 a - 129\) , \( 470 a + 555\bigr] \)
6272.7-d3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 46 a + 10\) , \( -4 a - 244\bigr] \)
6272.7-d4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -19 a - 7\) , \( 85 a - 27\bigr] \)
6272.7-d5	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 39 a - 174\) , \( -23 a + 980\bigr] \)
6272.7-d6	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -31 a + 36\) , \( -37 a + 126\bigr] \)

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