Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-175.1-e
Conductor 175.1
Rank \( 2 \)

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 175.1-e over \(\Q(\sqrt{14}) \)

Isogeny class 175.1-e contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
175.1-e1 \( \bigl[0\) , \( a\) , \( 1\) , \( 15760 a - 58964\) , \( -2198865 a + 8227401\bigr] \)
175.1-e2 \( \bigl[0\) , \( -a\) , \( 1\) , \( -160 a - 594\) , \( -2165 a - 8099\bigr] \)
175.1-e3 \( \bigl[0\) , \( a\) , \( 1\) , \( -1040 a + 3896\) , \( -4729 a + 17696\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph