Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-144.1-a
Conductor 144.1
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 144.1-a over \(\Q(\zeta_{15})^+\)

Isogeny class 144.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
144.1-a1 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - 3 a\) , \( -9953 a^{3} - 8233 a^{2} + 24770 a + 5451\) , \( 3556183 a^{3} + 2941287 a^{2} - 8850732 a - 1946362\bigr] \)
144.1-a2 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - 3 a\) , \( -294113 a^{3} - 243273 a^{2} + 731970 a + 160971\) , \( 118524887 a^{3} + 98030887 a^{2} - 294988204 a - 64870810\bigr] \)
144.1-a3 \( \bigl[a^{2} - 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 2 a\) , \( -a^{3} - 3 a^{2} + 2 a + 6\) , \( -4 a^{2} + 3 a + 3\bigr] \)
144.1-a4 \( \bigl[a^{2} - 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 2 a\) , \( -11 a^{3} - 33 a^{2} + 52 a + 16\) , \( -20 a^{3} - 134 a^{2} + 183 a + 43\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph