Properties

Base field 4.4.17600.1
Label 4.4.17600.1-4.1-d
Conductor 4.1
Rank \( 1 \)

Related objects

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Base field 4.4.17600.1

Generator \(a\), with minimal polynomial \( x^{4} - 14 x^{2} + 44 \); class number \(1\).

Elliptic curves in class 4.1-d over 4.4.17600.1

Isogeny class 4.1-d contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
4.1-d1 \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 4\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 5\) , \( 0\) , \( \frac{45}{2} a^{3} + 45 a^{2} - 207 a - 432\) , \( 309 a^{3} + 656 a^{2} - 2888 a - 6218\bigr] \)
4.1-d2 \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 4\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 5\) , \( 0\) , \( -\frac{5}{2} a^{3} - 5 a^{2} + 23 a + 48\) , \( -2 a^{3} - 4 a^{2} + 20 a + 42\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph