Properties

Base field 4.4.4913.1
Label 4.4.4913.1-4.2-a
Conductor 4.2
Rank \( 0 \)

Related objects

Learn more

Base field 4.4.4913.1

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

Elliptic curves in class 4.2-a over 4.4.4913.1

Isogeny class 4.2-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
4.2-a1 \( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( 2 a^{3} - a^{2} - 11 a - 3\) , \( -\frac{7}{2} a^{3} + 2 a^{2} + 23 a + \frac{13}{2}\bigr] \)
4.2-a2 \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{1}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( -\frac{35}{2} a^{3} + 25 a^{2} + 90 a - \frac{95}{2}\) , \( -\frac{29}{2} a^{3} - 41 a^{2} + 284 a - \frac{257}{2}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph