Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-63075.1-c
Conductor 63075.1
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 63075.1-c over \(\Q(\sqrt{-3}) \)

Isogeny class 63075.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
63075.1-c1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -390 a + 390\) , \( -4275\bigr] \)
63075.1-c2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -30 a + 30\) , \( -45\bigr] \)
63075.1-c3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -435 a + 435\) , \( -3528\bigr] \)
63075.1-c4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -6960 a + 6960\) , \( -224073\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph