Elliptic curve isogeny class 448.4-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-448.4-b
• Conductor: 448.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 448.4-b over \(\Q(\sqrt{-7}) \)

Isogeny class 448.4-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
448.4-b1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \)
448.4-b2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a - 6\) , \( -2 a - 4\bigr] \)
448.4-b3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 10\) , \( 6 a - 16\bigr] \)
448.4-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -40\) , \( -84\bigr] \)

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