Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-12337.2-c
Conductor 12337.2
Rank \( 0 \)

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 12337.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 12337.2-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
12337.2-c1 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -180 a + 29\) , \( 856 a - 560\bigr] \)
12337.2-c2 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 40 a + 39\) , \( 226 a - 266\bigr] \)
12337.2-c3 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -140 a - 46\) , \( 835 a - 1260\bigr] \)
12337.2-c4 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 5 a - 1\) , \( 9 a - 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph