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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3872.14-a
• Conductor: 3872.14
• Rank: \( 1 \)

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

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

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

Isogeny class 3872.14-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3872.14-a1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -6 a + 2\) , \( 0\bigr] \)
3872.14-a2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 24 a - 8\) , \( -18 a - 26\bigr] \)
3872.14-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 3 a - 24\) , \( -22 a + 46\bigr] \)
3872.14-a4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2 a + 22\) , \( 26 a - 14\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph