Elliptic curve isogeny class 16128.5-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-16128.5-a
• Conductor: 16128.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 16128.5-a over \(\Q(\sqrt{-7}) \)

Isogeny class 16128.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
16128.5-a1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 13 a + 170\) , \( -644 a + 460\bigr] \)
16128.5-a2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 213 a - 110\) , \( -2548 a - 868\bigr] \)
16128.5-a3	\( \bigl[0\) , \( a\) , \( 0\) , \( -69 a - 25\) , \( 300 a + 92\bigr] \)
16128.5-a4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 543 a - 261\) , \( -3960 a - 3060\bigr] \)

Rank

Rank: \( 0 \)

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