Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-30492.5-r
Conductor 30492.5
Rank \( 1 \)

Related objects

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

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

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

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

Curve label Weierstrass Coefficients
30492.5-r1 \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 45 a + 614\) , \( 4868 a - 3639\bigr] \)
30492.5-r2 \( \bigl[1\) , \( a\) , \( a\) , \( -46 a + 660\) , \( -4869 a + 1230\bigr] \)
30492.5-r3 \( \bigl[1\) , \( 1\) , \( 1\) , \( -405\) , \( 4731\bigr] \)
30492.5-r4 \( \bigl[1\) , \( 1\) , \( 1\) , \( -7445\) , \( 244091\bigr] \)

Rank

Rank: \( 1 \)

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