Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-3600.1-p
Conductor 3600.1
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 3600.1-p over \(\Q(\sqrt{3}) \)

Isogeny class 3600.1-p contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
3600.1-p1 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 3373 a - 5846\) , \( 1203326 a - 2084223\bigr] \)
3600.1-p2 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3347 a + 5794\) , \( -28024 a + 48537\bigr] \)
3600.1-p3 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 853 a - 1481\) , \( -3169 a + 5487\bigr] \)
3600.1-p4 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 8413 a - 14576\) , \( 552248 a - 956523\bigr] \)
3600.1-p5 \( \bigl[0\) , \( a\) , \( 0\) , \( 184 a - 321\) , \( -1907 a + 3299\bigr] \)
3600.1-p6 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 134413 a - 232826\) , \( 35343098 a - 61216023\bigr] \)

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