Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-145.3-f
Conductor 145.3
Rank \( 0 \)

Related objects

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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 145.3-f over \(\Q(\zeta_{15})^+\)

Isogeny class 145.3-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
145.3-f1 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - 4 a\) , \( a + 1\) , \( -2 a^{3} - 188 a^{2} + 310 a - 79\) , \( 1231 a^{3} - 2720 a^{2} + 732 a + 947\bigr] \)
145.3-f2 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - 4 a\) , \( a + 1\) , \( -2 a^{3} - 3 a^{2} + 5 a + 1\) , \( 4 a^{3} + 2 a^{2} - 10 a - 3\bigr] \)
145.3-f3 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - 4 a\) , \( a + 1\) , \( -37 a^{3} - 43 a^{2} + 110 a + 16\) , \( 207 a^{3} + 112 a^{2} - 455 a - 91\bigr] \)
145.3-f4 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - 4 a\) , \( a + 1\) , \( -632 a^{3} - 538 a^{2} + 1590 a + 351\) , \( 12035 a^{3} + 9884 a^{2} - 29902 a - 6541\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph