Properties

Base field \(\Q(\sqrt{5}, \sqrt{6})\)
Label 4.4.14400.1-5.1-a
Conductor 5.1
Rank \( 0 \)

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Base field \(\Q(\sqrt{5}, \sqrt{6})\)

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 13 x^{2} + 14 x + 19 \); class number \(1\).

Elliptic curves in class 5.1-a over \(\Q(\sqrt{5}, \sqrt{6})\)

Isogeny class 5.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
5.1-a1 \( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( -\frac{3}{19} a^{3} - \frac{5}{19} a^{2} + \frac{46}{19} a + 1\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( -\frac{454}{19} a^{3} + \frac{1270}{19} a^{2} + \frac{4827}{19} a - 535\) , \( -\frac{2934}{19} a^{3} + \frac{8296}{19} a^{2} + \frac{31232}{19} a - 3525\bigr] \)
5.1-a2 \( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} + \frac{10}{19} a + 5\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{14}{19} a^{3} - \frac{17}{19} a^{2} + \frac{88}{19} a + 14\) , \( -\frac{32}{19} a^{3} - \frac{104}{19} a^{2} + \frac{174}{19} a + 17\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph