Properties

Base field 4.4.13888.1
Label 4.4.13888.1-7.1-a
Conductor 7.1
Rank \( 0 \)

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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 7.1-a over 4.4.13888.1

Isogeny class 7.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
7.1-a1 \( \bigl[a\) , \( -a^{2} + 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{5}{3} a^{3} + \frac{7}{3} a^{2} + \frac{20}{3} a - 4\) , \( -\frac{14}{3} a^{3} + \frac{37}{3} a^{2} + \frac{50}{3} a - 39\bigr] \)
7.1-a2 \( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{4}{3} a + 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 2\) , \( -12 a^{3} + 35 a^{2} + 49 a - 124\) , \( -\frac{266}{3} a^{3} + \frac{688}{3} a^{2} + \frac{1274}{3} a - 704\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph