Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-23716.4-e
Conductor 23716.4
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 23716.4-e over \(\Q(\sqrt{-7}) \)

Isogeny class 23716.4-e contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
23716.4-e1 \( \bigl[1\) , \( a\) , \( 1\) , \( -9 a - 5\) , \( 13 a - 4\bigr] \)
23716.4-e2 \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -12 a + 6\) , \( 12 a - 22\bigr] \)
23716.4-e3 \( \bigl[1\) , \( a\) , \( 1\) , \( 361 a - 505\) , \( -787 a + 1306\bigr] \)
23716.4-e4 \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 178 a + 436\) , \( -1168 a + 428\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph