Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-14.1-b
Conductor 14.1
Rank not recorded

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

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

Elliptic curves in class 14.1-b over \(\Q(\sqrt{14}) \)

Isogeny class 14.1-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
14.1-b1 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 20462 a - 76559\) , \( -3121544 a + 11679749\bigr] \)
14.1-b2 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 62 a - 229\) , \( 960 a - 3591\bigr] \)
14.1-b3 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( -538 a + 2016\) , \( -21216 a + 79384\bigr] \)
14.1-b4 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 4262 a - 15944\) , \( -246560 a + 922544\bigr] \)
14.1-b5 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 1262 a - 4719\) , \( 45312 a - 169541\bigr] \)
14.1-b6 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 327662 a - 1225999\) , \( -197976456 a + 740760069\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph