Properties

Base field 3.3.1492.1
Label 3.3.1492.1-14.1-b
Conductor 14.1
Rank \( 1 \)

Related objects

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Base field 3.3.1492.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 9 x - 5 \); class number \(1\).

Elliptic curves in class 14.1-b over 3.3.1492.1

Isogeny class 14.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
14.1-b1 \( \bigl[1\) , \( -a - 1\) , \( a^{2} - a - 5\) , \( -5 a^{2} + 15 a + 13\) , \( 10 a^{2} - 32 a - 28\bigr] \)
14.1-b2 \( \bigl[1\) , \( -a - 1\) , \( a^{2} - a - 5\) , \( -75 a^{2} + 235 a + 173\) , \( 716 a^{2} - 2238 a - 1692\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph