Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-14400.1-b
Conductor 14400.1
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 14400.1-b over \(\Q(\sqrt{-7}) \)

Isogeny class 14400.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
14400.1-b1 \( \bigl[a\) , \( 1\) , \( a\) , \( 45 a - 32\) , \( 129 a + 17\bigr] \)
14400.1-b2 \( \bigl[a\) , \( 1\) , \( a\) , \( -2\) , \( 3 a + 5\bigr] \)
14400.1-b3 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a + 6\) , \( -4 a + 8\bigr] \)
14400.1-b4 \( \bigl[a\) , \( -1\) , \( a\) , \( 13 a - 12\) , \( 17 a + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph