Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-2304.1-u
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-u over \(\Q(\sqrt{3}) \)

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

Curve label Weierstrass Coefficients
2304.1-u1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 56601488 a - 98036652\) , \( 303715215440 a - 526050184174\bigr] \)
2304.1-u2 \( \bigl[0\) , \( -a\) , \( 0\) , \( 1527032 a - 2644896\) , \( -1350928288 a + 2339876432\bigr] \)
2304.1-u3 \( \bigl[0\) , \( -a\) , \( 0\) , \( 95492 a - 165396\) , \( -21042496 a + 36446672\bigr] \)
2304.1-u4 \( \bigl[0\) , \( -a\) , \( 0\) , \( 1583386 a - 2742504\) , \( -176024176 a + 304882816\bigr] \)
2304.1-u5 \( \bigl[0\) , \( -a\) , \( 0\) , \( 312 a - 552\) , \( -13308 a + 23040\bigr] \)
2304.1-u6 \( \bigl[0\) , \( -a\) , \( 0\) , \( -6279224 a + 10875936\) , \( -1413453664 a + 2448173560\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph