Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-2304.1-e
Conductor 2304.1
Rank \( 0 \)

Related objects

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

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

Elliptic curves in class 2304.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 2304.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
2304.1-e1 \( \bigl[0\) , \( a\) , \( 0\) , \( -312 a - 552\) , \( 13308 a + 23040\bigr] \)
2304.1-e2 \( \bigl[0\) , \( a\) , \( 0\) , \( 43288 a - 74976\) , \( -6476960 a + 11218424\bigr] \)
2304.1-e3 \( \bigl[0\) , \( a\) , \( 0\) , \( 2758 a - 4776\) , \( -98288 a + 170240\bigr] \)
2304.1-e4 \( \bigl[0\) , \( a\) , \( 0\) , \( -9304 a + 16116\) , \( -2793284 a + 4838110\bigr] \)
2304.1-e5 \( \bigl[0\) , \( a\) , \( 0\) , \( 44 a - 84\) , \( 160 a - 272\bigr] \)
2304.1-e6 \( \bigl[0\) , \( a\) , \( 0\) , \( -136 a + 96\) , \( 1312 a - 1712\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph