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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-14400.4-d
• 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-d over \(\Q(\sqrt{-7}) \)

Isogeny class 14400.4-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14400.4-d1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 4\) , \( 0\bigr] \)
14400.4-d2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -16\) , \( -16\bigr] \)
14400.4-d3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -136\) , \( 560\bigr] \)
14400.4-d4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -216\) , \( -1296\bigr] \)

Rank

Rank: \( 1 \)

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