Elliptic curve isogeny class 3872.5-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3872.5-b
• Conductor: 3872.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 3872.5-b over \(\Q(\sqrt{-7}) \)

Isogeny class 3872.5-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3872.5-b1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9 a + 23\) , \( 0\bigr] \)
3872.5-b2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -12 a - 7\) , \( a + 10\bigr] \)
3872.5-b3	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -102 a - 107\) , \( 867 a + 190\bigr] \)
3872.5-b4	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -69 a + 223\) , \( -684 a - 536\bigr] \)
3872.5-b5	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -42 a - 19\) , \( 205 a - 62\bigr] \)
3872.5-b6	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -33 a + 71\) , \( -78 a - 204\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph