Elliptic curve isogeny class 34848.3-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-34848.3-d
• Conductor: 34848.3
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

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

Elliptic curves in class 34848.3-d over \(\Q(\sqrt{-7}) \)

Isogeny class 34848.3-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
34848.3-d1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 7 a + 1\) , \( 15 a - 54\bigr] \)
34848.3-d2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -113 a + 106\) , \( 198 a - 804\bigr] \)
34848.3-d3	\( \bigl[a\) , \( a\) , \( 0\) , \( 32 a + 8\) , \( 15 a - 162\bigr] \)
34848.3-d4	\( \bigl[a\) , \( -1\) , \( 0\) , \( 152 a + 101\) , \( 310 a - 1870\bigr] \)