Elliptic curve isogeny class 3584.4-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3584.4-e
• Conductor: 3584.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 3584.4-e over \(\Q(\sqrt{-7}) \)

Isogeny class 3584.4-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3584.4-e1	\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 2\) , \( 2 a + 4\bigr] \)
3584.4-e2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -59 a + 118\) , \( -138 a - 276\bigr] \)
3584.4-e3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -19 a + 38\) , \( 30 a + 60\bigr] \)
3584.4-e4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 10 a - 8\) , \( 13 a + 2\bigr] \)
3584.4-e5	\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 14\) , \( -2 a + 20\bigr] \)
3584.4-e6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -299 a + 598\) , \( 1990 a + 3980\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph