Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-252.1-b
Conductor 252.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{14}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 14 \); class number \(1\).

Elliptic curves in class 252.1-b over \(\Q(\sqrt{14}) \)

Isogeny class 252.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
252.1-b1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -113\) , \( -516\bigr] \)
252.1-b2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 7\) , \( 0\bigr] \)
252.1-b3 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -853 a - 3169\) , \( -8575 a - 32064\bigr] \)
252.1-b4 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 54853 a - 205219\) , \( 13539589 a - 50660484\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph