Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-145.2-b
Conductor 145.2
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 145.2-b over \(\Q(\zeta_{15})^+\)

Isogeny class 145.2-b contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
145.2-b1 \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{2} + a + 1\) , \( a + 1\) , \( 6 a^{3} + 6 a^{2} - 16 a - 6\) , \( 12 a^{3} + 9 a^{2} - 33 a - 10\bigr] \)
145.2-b2 \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{2} + a + 1\) , \( a + 1\) , \( a^{3} + a^{2} - 6 a - 1\) , \( a^{3} - a^{2} - 4 a - 1\bigr] \)
145.2-b3 \( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} + a - 1\) , \( -2217840 a^{3} - 1835159 a^{2} + 5518084 a + 1213528\) , \( 2470158781 a^{3} + 2043066146 a^{2} - 6147760682 a - 1351954420\bigr] \)
145.2-b4 \( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} + a - 1\) , \( -2217835 a^{3} - 1835159 a^{2} + 5518064 a + 1213533\) , \( 2470158335 a^{3} + 2043065677 a^{2} - 6147759783 a - 1351954219\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph