Elliptic curve isogeny class 3872.14-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3872.14-c
• Conductor: 3872.14
• Rank: \( 0 \)

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

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

Elliptic curves in class 3872.14-c over \(\Q(\sqrt{-7}) \)

Isogeny class 3872.14-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3872.14-c1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -471 a - 938\) , \( -9387 a - 9491\bigr] \)
3872.14-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -11 a + 6\) , \( 5 a - 73\bigr] \)
3872.14-c3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 17 a - 31\) , \( -13 a - 33\bigr] \)
3872.14-c4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -18 a - 12\) , \( -36 a + 19\bigr] \)
3872.14-c5	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -31 a - 58\) , \( -147 a - 163\bigr] \)
3872.14-c6	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 157 a - 351\) , \( 1387 a - 2265\bigr] \)

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