Properties

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

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

Curve label Weierstrass Coefficients
145.2-f1 \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 2\) , \( 935 a^{3} + 306 a^{2} - 3343 a - 705\) , \( -17303 a^{3} - 5897 a^{2} + 61256 a + 12892\bigr] \)
145.2-f2 \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 2\) , \( 35 a^{3} + a^{2} - 148 a - 35\) , \( -338 a^{3} - 165 a^{2} + 1084 a + 222\bigr] \)
145.2-f3 \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 2\) , \( a^{2} - 3 a - 5\) , \( -6 a^{3} - a^{2} + 18 a - 5\bigr] \)
145.2-f4 \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 2\) , \( -305 a^{3} - 304 a^{2} + 727 a + 155\) , \( -5961 a^{3} - 4729 a^{2} + 14976 a + 3280\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph