Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-18396.2-c
Conductor 18396.2
Rank \( 1 \)

Related objects

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

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

Elliptic curves in class 18396.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 18396.2-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
18396.2-c1 \( \bigl[a\) , \( a\) , \( a + 1\) , \( 29 a - 34\) , \( 78 a - 63\bigr] \)
18396.2-c2 \( \bigl[a\) , \( a\) , \( a + 1\) , \( -a - 4\) , \( 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph