Properties

Base field 4.4.4525.1
Label 4.4.4525.1-45.4-c
Conductor 45.4
Rank \( 1 \)

Related objects

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Base field 4.4.4525.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 3 x + 9 \); class number \(1\).

Elliptic curves in class 45.4-c over 4.4.4525.1

Isogeny class 45.4-c contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
45.4-c1 \( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + \frac{4}{3} a - 3\) , \( a^{2} - 4\) , \( -\frac{4}{3} a^{3} + \frac{1}{3} a^{2} + \frac{25}{3} a + 4\) , \( -\frac{5}{3} a^{3} - \frac{4}{3} a^{2} + \frac{32}{3} a + 13\bigr] \)
45.4-c2 \( \bigl[a^{2} - 3\) , \( \frac{1}{3} a^{3} - \frac{4}{3} a^{2} - \frac{1}{3} a + 3\) , \( a\) , \( \frac{10}{3} a^{3} + \frac{8}{3} a^{2} - \frac{73}{3} a - 24\) , \( -8 a^{3} - 6 a^{2} + 53 a + 60\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph