Elliptic curve isogeny class 3872.6-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3872.6-a
• Conductor: 3872.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 3872.6-a over \(\Q(\sqrt{-7}) \)

Isogeny class 3872.6-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
3872.6-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -8 a + 44\) , \( -71 a + 5\bigr] \)
3872.6-a2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -243 a + 174\) , \( -970 a + 2531\bigr] \)
3872.6-a3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 76 a - 135\) , \( 735 a - 200\bigr] \)
3872.6-a4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -9 a + 15\) , \( -18 a - 10\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph