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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-30492.5-b
• 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-b over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
30492.5-b1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1676\) , \( 5058506\bigr] \)
30492.5-b2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -30530 a + 116775\) , \( 8742315 a + 2999296\bigr] \)
30492.5-b3	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 30529 a + 86246\) , \( -8742316 a + 11741612\bigr] \)
30492.5-b4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -452236\) , \( 115355594\bigr] \)

Rank

Rank: \( 0 \)

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