Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-22.2-a
Conductor 22.2
Rank not recorded

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Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 22.2-a over \(\Q(\sqrt{3}) \)

Isogeny class 22.2-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
22.2-a1 \( \bigl[1\) , \( 0\) , \( 1\) , \( 1813 a - 3142\) , \( -55168 a + 95554\bigr] \)
22.2-a2 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -18 a - 33\) , \( -83 a - 145\bigr] \)
22.2-a3 \( \bigl[1\) , \( 0\) , \( 1\) , \( 1688 a - 2922\) , \( -63194 a + 109458\bigr] \)
22.2-a4 \( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a + 2\) , \( a + 1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph