Elliptic curve isogeny class 3200.4-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3200.4-c
• Conductor: 3200.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 3200.4-c over \(\Q(\sqrt{-7}) \)

Isogeny class 3200.4-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3200.4-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -12 a - 4\) , \( 28 a - 8\bigr] \)
3200.4-c2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 12 a - 16\) , \( 28 a - 20\bigr] \)
3200.4-c3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 6\) , \( 6 a\bigr] \)
3200.4-c4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 34\) , \( 30 a - 32\bigr] \)

Rank

Rank: \( 1 \)

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