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

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

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

Curve label	Weierstrass Coefficients
3872.14-d1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 30 a + 86\) , \( -500 a - 580\bigr] \)
3872.14-d2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 46 a - 113\) , \( -353 a - 833\bigr] \)
3872.14-d3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 138 a + 159\) , \( 623 a - 1831\bigr] \)
3872.14-d4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 178 a - 265\) , \( -1275 a + 703\bigr] \)
3872.14-d5	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 2138 a + 2479\) , \( 46031 a - 123975\bigr] \)
3872.14-d6	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2738 a - 4105\) , \( -87547 a + 61119\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph