Properties

Base field 4.4.13888.1
Label 4.4.13888.1-7.3-b
Conductor 7.3
Rank not recorded

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Base field 4.4.13888.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 6 x + 9 \); class number \(1\).

Elliptic curves in class 7.3-b over 4.4.13888.1

Isogeny class 7.3-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
7.3-b1 \( \bigl[a^{2} - 4\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{11}{3} a^{3} + \frac{28}{3} a^{2} + \frac{44}{3} a - 34\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{7}{3} a + 4\bigr] \)
7.3-b2 \( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{4}{3} a + 2\) , \( -a^{2} + 2 a + 5\) , \( a\) , \( -3 a^{3} + 6 a^{2} + 17 a - 18\) , \( \frac{5}{3} a^{3} - \frac{16}{3} a^{2} - \frac{29}{3} a + 28\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph