Elliptic curve isogeny class 14400.4-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-14400.4-c
• Conductor: 14400.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 14400.4-c over \(\Q(\sqrt{-7}) \)

Isogeny class 14400.4-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
14400.4-c1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -2400\bigr] \)
14400.4-c2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 80\) , \( 80\bigr] \)
14400.4-c3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -20\) , \( 0\bigr] \)
14400.4-c4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -200\) , \( -1152\bigr] \)
14400.4-c5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \)
14400.4-c6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -3200\) , \( -70752\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph