Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-11025.3-c
Conductor 11025.3
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 11025.3-c over \(\Q(\sqrt{-3}) \)

Isogeny class 11025.3-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
11025.3-c1 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -988 a - 1651\) , \( 48169 a + 42560\bigr] \)
11025.3-c2 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 2 a - 1\) , \( -11 a - 10\bigr] \)
11025.3-c3 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 317 a + 524\) , \( 3139 a + 2153\bigr] \)
11025.3-c4 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -88 a - 151\) , \( 169 a + 290\bigr] \)
11025.3-c5 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -43 a - 76\) , \( -341 a - 217\bigr] \)
11025.3-c6 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1213 a - 2026\) , \( 33919 a + 30815\bigr] \)
11025.3-c7 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -718 a - 1201\) , \( -17891 a - 14032\bigr] \)
11025.3-c8 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -19438 a - 32401\) , \( 2281669 a + 1971170\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph