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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3872.14-b
• 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-b over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
3872.14-b1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 12 a - 20\) , \( 11 a - 9\bigr] \)
3872.14-b2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 9 a + 13\) , \( 9 a + 13\bigr] \)
3872.14-b3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 69 a + 153\) , \( 753 a - 1067\bigr] \)
3872.14-b4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 102 a - 210\) , \( -765 a + 847\bigr] \)
3872.14-b5	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 33 a + 37\) , \( 111 a - 245\bigr] \)
3872.14-b6	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 42 a - 62\) , \( -163 a + 81\bigr] \)

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