Elliptic curve isogeny class 6300.2-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-6300.2-e
• Conductor: 6300.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 6300.2-e over \(\Q(\sqrt{-7}) \)

Isogeny class 6300.2-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
6300.2-e1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -980\) , \( -15325\bigr] \)
6300.2-e2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 10\) , \( -13\bigr] \)
6300.2-e3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -205\bigr] \)
6300.2-e4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -370\) , \( 2435\bigr] \)
6300.2-e5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -1050\) , \( -13533\bigr] \)
6300.2-e6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -16800\) , \( -845133\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph