Properties

Base field 4.4.13968.1
Label 4.4.13968.1-13.1-b
Conductor 13.1
Rank \( 1 \)

Related objects

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Base field 4.4.13968.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 4 \); class number \(1\).

Elliptic curves in class 13.1-b over 4.4.13968.1

Isogeny class 13.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
13.1-b1 \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -4 a^{3} + 2 a^{2} + 33 a + 12\) , \( -13 a^{3} + \frac{17}{2} a^{2} + \frac{205}{2} a + 29\bigr] \)
13.1-b2 \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( a^{3} - a^{2} + 3 a - 7\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 18 a - 26\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph