Elliptic curve isogeny class 12800.4-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-12800.4-b
• Conductor: 12800.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 12800.4-b over \(\Q(\sqrt{-7}) \)

Isogeny class 12800.4-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
12800.4-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -28 a + 8\) , \( 64 a - 96\bigr] \)
12800.4-b2	\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a + 32\) , \( 76 a - 72\bigr] \)
12800.4-b3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 11\) , \( 7 a - 13\bigr] \)
12800.4-b4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 34 a - 69\) , \( 127 a - 125\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph