Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-114244.3-j
Conductor 114244.3
Rank \( 0 \)

Related objects

Learn more

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

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

Elliptic curves in class 114244.3-j over \(\Q(\sqrt{-3}) \)

Isogeny class 114244.3-j contains 5 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
114244.3-j1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -77659 a + 77659\) , \( -8336303\bigr] \)
114244.3-j2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -764 a + 764\) , \( -16264\bigr] \)
114244.3-j3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 81 a - 81\) , \( 467\bigr] \)
114244.3-j4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -15974 a - 22896\) , \( -1629498 a - 1117130\bigr] \)
114244.3-j5 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 22896 a + 15974\) , \( 1629498 a - 2746628\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 3 & 9 & 9 & 9 \\ 3 & 1 & 3 & 3 & 3 \\ 9 & 3 & 1 & 9 & 9 \\ 9 & 3 & 9 & 1 & 9 \\ 9 & 3 & 9 & 9 & 1 \end{array}\right)\)

Isogeny graph