Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-112.1-f
Conductor 112.1
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 112.1-f over \(\Q(\sqrt{14}) \)

Isogeny class 112.1-f contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
112.1-f1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 81847 a - 306244\) , \( -24502404 a + 91679601\bigr] \)
112.1-f2 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 247 a - 924\) , \( 9108 a - 34079\bigr] \)
112.1-f3 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2153 a + 8056\) , \( -182080 a + 681281\bigr] \)
112.1-f4 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 17047 a - 63784\) , \( -1874592 a + 7014081\bigr] \)
112.1-f5 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 5047 a - 18884\) , \( 391484 a - 1464799\bigr] \)
112.1-f6 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1310647 a - 4904004\) , \( -1576286340 a + 5897923441\bigr] \)

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