Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-3388.5-b
Conductor 3388.5
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 3388.5-b over \(\Q(\sqrt{-7}) \)

Isogeny class 3388.5-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
3388.5-b1 \( \bigl[1\) , \( 1\) , \( 0\) , \( -14\) , \( -28\bigr] \)
3388.5-b2 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -2 a - 6\) , \( -4 a - 8\bigr] \)
3388.5-b3 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( a - 7\) , \( 3 a - 11\bigr] \)
3388.5-b4 \( \bigl[1\) , \( 1\) , \( 0\) , \( -234\) , \( -1480\bigr] \)

Rank

Rank: \( 1 \)

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