Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-1458.1-i
Conductor 1458.1
Rank not recorded

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 1458.1-i over \(\Q(\sqrt{3}) \)

Isogeny class 1458.1-i contains 4 curves linked by isogenies of degrees dividing 21.

Curve label Weierstrass Coefficients
1458.1-i1 \( \bigl[a\) , \( 0\) , \( 1\) , \( 60322 a - 104487\) , \( -10598940 a + 18357906\bigr] \)
1458.1-i2 \( \bigl[a\) , \( 0\) , \( a\) , \( -6\) , \( -6\bigr] \)
1458.1-i3 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 5302 a - 9185\) , \( -563243 a + 975564\bigr] \)
1458.1-i4 \( \bigl[1\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 21 & 3 & 7 \\ 21 & 1 & 7 & 3 \\ 3 & 7 & 1 & 21 \\ 7 & 3 & 21 & 1 \end{array}\right)\)

Isogeny graph