Elliptic curve isogeny class 34848.13-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-34848.13-a
• Conductor: 34848.13
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 34848.13-a over \(\Q(\sqrt{-7}) \)

Isogeny class 34848.13-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
34848.13-a1	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -9086 a + 5890\) , \( 223030 a - 519286\bigr] \)
34848.13-a2	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -41 a - 5\) , \( 532 a - 1696\bigr] \)
34848.13-a3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 49 a + 2950\) , \( 49752 a - 18240\bigr] \)
34848.13-a4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -386 a + 55\) , \( 3159 a - 3477\bigr] \)