Elliptic curve isogeny class 34848.5-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-34848.5-e
• Conductor: 34848.5
• Rank: \( 0 \)

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

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

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

Elliptic curves in class 34848.5-e over \(\Q(\sqrt{-7}) \)

Isogeny class 34848.5-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
34848.5-e1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 11 a - 62\) , \( -36 a + 182\bigr] \)
34848.5-e2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 12 a - 1\) , \( 19 a - 5\bigr] \)
34848.5-e3	\( \bigl[a\) , \( -a\) , \( 0\) , \( 7 a - 18\) , \( 17 a - 6\bigr] \)
34848.5-e4	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 72 a + 59\) , \( 247 a - 689\bigr] \)