Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-3750.1-e
Conductor 3750.1
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 3750.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 3750.1-e contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
3750.1-e1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( -3\bigr] \)
3750.1-e2 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1568 a - 2716\) , \( -212160 a + 367472\bigr] \)
3750.1-e3 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 46368 a - 80316\) , \( -7076160 a + 12256272\bigr] \)
3750.1-e4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -53\) , \( -153\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph