Elliptic curve isogeny class 18432.7-g over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-18432.7-g
• Conductor: 18432.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 18432.7-g over \(\Q(\sqrt{-7}) \)

Isogeny class 18432.7-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
18432.7-g1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -29 a + 14\) , \( 57 a - 98\bigr] \)
18432.7-g2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a + 8\) , \( 4 a - 12\bigr] \)
18432.7-g3	\( \bigl[0\) , \( -1\) , \( 0\) , \( a + 4\) , \( 5 a - 6\bigr] \)
18432.7-g4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 16 a + 79\) , \( 224 a - 255\bigr] \)

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