Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-746.1-c
Number of curves 2
Graph
Conductor 746.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 746.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 746.1-c contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
746.1-c1 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2\) , \( a + 1\bigr] \)
746.1-c2 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 3\) , \( -31 a - 41\bigr] \)