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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3872.5-c
• 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-c over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
3872.5-c1	\( \bigl[a\) , \( 1\) , \( a\) , \( 469 a - 1407\) , \( 9386 a - 18877\bigr] \)
3872.5-c2	\( \bigl[a\) , \( -1\) , \( a\) , \( 9 a - 3\) , \( -6 a - 67\bigr] \)
3872.5-c3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -17 a - 13\) , \( 0\bigr] \)
3872.5-c4	\( \bigl[a\) , \( a\) , \( a\) , \( 18 a - 29\) , \( 6 a - 23\bigr] \)
3872.5-c5	\( \bigl[a\) , \( 1\) , \( a\) , \( 29 a - 87\) , \( 146 a - 309\bigr] \)
3872.5-c6	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -157 a - 193\) , \( -1580 a - 372\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph