Elliptic curve isogeny class 3584.7-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3584.7-b
• Conductor: 3584.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 3584.7-b over \(\Q(\sqrt{-7}) \)

Isogeny class 3584.7-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3584.7-b1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 0\) , \( 4 a - 12\bigr] \)
3584.7-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 14 a - 3\) , \( -13 a - 14\bigr] \)
3584.7-b3	\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a + 17\) , \( 29 a - 18\bigr] \)
3584.7-b4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 40 a + 40\) , \( 84 a - 252\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph