Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-3528.1-h
Conductor 3528.1
Rank \( 2 \)

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 3528.1-h over \(\Q(\sqrt{3}) \)

Isogeny class 3528.1-h contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
3528.1-h1 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -10 a + 16\) , \( -41 a + 70\bigr] \)
3528.1-h2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( 5\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph