Properties

Base field 3.3.1492.1
Label 3.3.1492.1-16.1-c
Conductor 16.1
Rank \( 0 \)

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 16.1-c over 3.3.1492.1

Isogeny class 16.1-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
16.1-c1 \( \bigl[a + 1\) , \( -a^{2} + 2 a + 7\) , \( a^{2} - 2 a - 5\) , \( 5 a^{2} - 18 a - 3\) , \( 315 a^{2} - 990 a - 741\bigr] \)
16.1-c2 \( \bigl[a + 1\) , \( -a^{2} + 2 a + 7\) , \( a^{2} - 2 a - 5\) , \( -20 a^{2} + 62 a + 57\) , \( 101 a^{2} - 315 a - 234\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph