Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-3750.1-c
Conductor 3750.1
Rank \( 1 \)

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 3750.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 3750.1-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
3750.1-c1 \( \bigl[a\) , \( 1\) , \( 0\) , \( -337\) , \( 7631\bigr] \)
3750.1-c2 \( \bigl[a\) , \( 1\) , \( 0\) , \( 38\) , \( -244\bigr] \)
3750.1-c3 \( \bigl[a\) , \( 1\) , \( 0\) , \( -11337\) , \( 56631\bigr] \)
3750.1-c4 \( \bigl[a\) , \( 1\) , \( 0\) , \( -1712\) , \( 22506\bigr] \)
3750.1-c5 \( \bigl[a\) , \( 1\) , \( 0\) , \( -462\) , \( -3744\bigr] \)
3750.1-c6 \( \bigl[a\) , \( 1\) , \( 0\) , \( -8337\) , \( 287631\bigr] \)
3750.1-c7 \( \bigl[a\) , \( 1\) , \( 0\) , \( -7212\) , \( -239994\bigr] \)
3750.1-c8 \( \bigl[a\) , \( 1\) , \( 0\) , \( -133337\) , \( 18662631\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph