Elliptic curve isogeny class 12800.7-g over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-12800.7-g
• Conductor: 12800.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 12800.7-g over \(\Q(\sqrt{-7}) \)

Isogeny class 12800.7-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
12800.7-g1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -13 a - 13\) , \( 34 a - 102\bigr] \)
12800.7-g2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 7 a + 7\) , \( 6 a - 18\bigr] \)
12800.7-g3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 2\) , \( -a + 3\bigr] \)
12800.7-g4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 107 a + 107\) , \( 426 a - 1278\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph