Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-56.1-d
Conductor 56.1
Rank \( 2 \)

Related objects

Learn more

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

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

Elliptic curves in class 56.1-d over \(\Q(\sqrt{14}) \)

Isogeny class 56.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
56.1-d1 \( \bigl[a\) , \( 1\) , \( a\) , \( 150 a - 635\) , \( 2318 a - 9041\bigr] \)
56.1-d2 \( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
56.1-d3 \( \bigl[a\) , \( 1\) , \( a\) , \( -15\) , \( -5\bigr] \)
56.1-d4 \( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -11\bigr] \)
56.1-d5 \( \bigl[a\) , \( 1\) , \( a\) , \( -75\) , \( -361\bigr] \)
56.1-d6 \( \bigl[a\) , \( 1\) , \( a\) , \( -150 a - 635\) , \( -2318 a - 9041\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 8 & 4 & 2 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 8 & 4 & 1 & 2 & 4 & 8 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 2 & 4 & 4 & 2 & 1 & 2 \\ 4 & 8 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph