Elliptic curve isogeny class 2048.7-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-2048.7-d
• Conductor: 2048.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 2048.7-d over \(\Q(\sqrt{-7}) \)

Isogeny class 2048.7-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2048.7-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 2\) , \( 0\bigr] \)
2048.7-d2	\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( 0\bigr] \)
2048.7-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 11 a + 11\) , \( 14 a - 42\bigr] \)
2048.7-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 11 a + 11\) , \( -14 a + 42\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph