Elliptic curve isogeny class 30492.5-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-30492.5-e
• Conductor: 30492.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 30492.5-e over \(\Q(\sqrt{-7}) \)

Isogeny class 30492.5-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
30492.5-e1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -1444\) , \( 410800\bigr] \)
30492.5-e2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -644\) , \( -2352\bigr] \)
30492.5-e3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -5764\) , \( 164560\bigr] \)
30492.5-e4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -92004\) , \( 10703088\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph