Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-25.1-b
Conductor 25.1
Rank \( 0 \)

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Base field \(\Q(\zeta_{15})^+\)

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

Elliptic curves in class 25.1-b over \(\Q(\zeta_{15})^+\)

Isogeny class 25.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
25.1-b1 \( \bigl[0\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -a + 2\) , \( -a^{2} - a + 3\bigr] \)
25.1-b2 \( \bigl[0\) , \( a^{3} - 2 a + 1\) , \( a^{2} - 1\) , \( a^{3} + a^{2} - 3 a\) , \( -11017 a^{3} - 9112 a^{2} + 27421 a + 6030\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph