Elliptic curve isogeny class 4032.1-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4032.1-b
• Conductor: 4032.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 4032.1-b over \(\Q(\sqrt{-7}) \)

Isogeny class 4032.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
4032.1-b1	\( \bigl[a\) , \( a\) , \( 0\) , \( -36 a + 59\) , \( -27 a - 145\bigr] \)
4032.1-b2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -21 a + 94\) , \( -214 a - 28\bigr] \)
4032.1-b3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -6 a + 4\) , \( -13 a + 14\bigr] \)
4032.1-b4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -10 a - 6\) , \( -20 a + 15\bigr] \)
4032.1-b5	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -15 a - 56\) , \( 22 a + 211\bigr] \)
4032.1-b6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -a - 38\) , \( 112\bigr] \)