Properties

Base field 3.3.1849.1
Label 3.3.1849.1-8.4-a
Conductor 8.4
Rank \( 1 \)

Related objects

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Base field 3.3.1849.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 14 x - 8 \); class number \(1\).

Elliptic curves in class 8.4-a over 3.3.1849.1

Isogeny class 8.4-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
8.4-a1 \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( 0\) , \( 0\) , \( -\frac{706755}{2} a^{2} + \frac{2748049}{2} a + 978825\) , \( 624298943 a^{2} - 2427421614 a - 1729218620\bigr] \)
8.4-a2 \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( -65 a^{2} + 274 a + 196\) , \( \frac{1799}{2} a^{2} - \frac{6895}{2} a - 2458\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph