Properties

Base field 4.4.19821.1
Label 4.4.19821.1-3.1-a
Conductor 3.1
Rank not recorded

Related objects

Learn more about

Base field 4.4.19821.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 3 \); class number \(1\).

Elliptic curves in class 3.1-a over 4.4.19821.1

Isogeny class 3.1-a contains 2 curves linked by isogenies of degree 11.

Curve label Weierstrass Coefficients
3.1-a1 \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a\) , \( a^{2} - 4\) , \( \frac{20753}{3} a^{3} + \frac{2342}{3} a^{2} - 54658 a - 19596\) , \( \frac{2144189}{3} a^{3} + \frac{227318}{3} a^{2} - 5636519 a - 1948781\bigr] \)
3.1-a2 \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a\) , \( a^{2} - 4\) , \( -\frac{7}{3} a^{3} + \frac{2}{3} a^{2} + 22 a + 9\) , \( -\frac{10}{3} a^{3} + \frac{5}{3} a^{2} + 32 a + 7\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph