Elliptic curve isogeny class 14400.1-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-14400.1-c
• Conductor: 14400.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 14400.1-c over \(\Q(\sqrt{-7}) \)

Isogeny class 14400.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14400.1-c1	\( \bigl[a\) , \( a\) , \( 0\) , \( -82 a + 171\) , \( -355 a - 573\bigr] \)
14400.1-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -22 a - 8\) , \( -69 a + 46\bigr] \)
14400.1-c3	\( \bigl[a\) , \( a\) , \( 0\) , \( -27 a + 1\) , \( -86 a + 85\bigr] \)
14400.1-c4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 25 a - 168\) , \( -262 a + 891\bigr] \)

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