Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-242.3-a
Conductor 242.3
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 242.3-a over \(\Q(\sqrt{-7}) \)

Isogeny class 242.3-a contains 4 curves linked by isogenies of degrees dividing 33.

Curve label Weierstrass Coefficients
242.3-a1 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -a - 5\) , \( a + 3\bigr] \)
242.3-a2 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -25 a - 49\) , \( -90 a - 142\bigr] \)
242.3-a3 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 10 a - 4\) , \( -7 a - 18\bigr] \)
242.3-a4 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -96 a - 300\) , \( 831 a + 2090\bigr] \)

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