Elliptic curve isogeny class 18432.6-g over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-18432.6-g
• Conductor: 18432.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 18432.6-g over \(\Q(\sqrt{-7}) \)

Isogeny class 18432.6-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
18432.6-g1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 11\) , \( -7 a + 3\bigr] \)
18432.6-g2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -a + 5\) , \( -5 a - 1\bigr] \)
18432.6-g3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 29 a - 15\) , \( -57 a - 41\bigr] \)
18432.6-g4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -16 a + 95\) , \( -224 a - 31\bigr] \)

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