Properties

Base field \(\Q(\sqrt{5}, \sqrt{7})\)
Label 4.4.19600.1-25.1-c
Conductor 25.1
Rank \( 1 \)

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Base field \(\Q(\sqrt{5}, \sqrt{7})\)

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 29 \); class number \(1\).

Elliptic curves in class 25.1-c over \(\Q(\sqrt{5}, \sqrt{7})\)

Isogeny class 25.1-c contains only one elliptic curve.

Curve label Weierstrass Coefficients
25.1-c1 \( \bigl[0\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{27}{23} a + \frac{106}{23}\) , \( -\frac{3}{23} a^{3} - \frac{7}{23} a^{2} + \frac{7}{23} a - \frac{79}{23}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph