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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-18432.6-c
• 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-c over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
18432.6-c1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 11\) , \( 3 a + 11\bigr] \)
18432.6-c2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 12\) , \( 8 a - 16\bigr] \)
18432.6-c3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 27 a - 2\) , \( -41 a - 74\bigr] \)
18432.6-c4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 32 a - 192\) , \( 296 a - 976\bigr] \)

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