Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-12348.2-b
Conductor 12348.2
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 12348.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 12348.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
12348.2-b1 \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 60 a + 36\) , \( 383 a - 768\bigr] \)
12348.2-b2 \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -5790 a - 3474\) , \( 69683 a - 123240\bigr] \)
12348.2-b3 \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 1560 a + 936\) , \( 7943 a - 16224\bigr] \)
12348.2-b4 \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 13710 a + 8226\) , \( -638437 a + 1167672\bigr] \)
12348.2-b5 \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 1260 a + 756\) , \( 17183 a - 33024\bigr] \)
12348.2-b6 \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 20160 a + 12096\) , \( 1128503 a - 2107488\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph