Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-242.4-a
Conductor 242.4
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 242.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 242.4-a contains 4 curves linked by isogenies of degrees dividing 33.

Curve label Weierstrass Coefficients
242.4-a1 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -5\) , \( -6 a + 4\bigr] \)
242.4-a2 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 24 a - 73\) , \( 90 a - 232\bigr] \)
242.4-a3 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -11 a + 7\) , \( 7 a - 25\bigr] \)
242.4-a4 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 95 a - 395\) , \( -1131 a + 2731\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 33 & 11 & 3 \\ 33 & 1 & 3 & 11 \\ 11 & 3 & 1 & 33 \\ 3 & 11 & 33 & 1 \end{array}\right)\)

Isogeny graph