Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-145.1-d
Conductor 145.1
Rank not recorded

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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 145.1-d over \(\Q(\zeta_{15})^+\)

Isogeny class 145.1-d contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
145.1-d1 \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( 1\) , \( a^{3} - 2 a\) , \( -70933 a^{3} - 60234 a^{2} + 173150 a + 38181\) , \( -15136874 a^{3} - 12573990 a^{2} + 37555267 a + 8262428\bigr] \)
145.1-d2 \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( 1\) , \( a^{3} - 2 a\) , \( -1183108 a^{3} - 980109 a^{2} + 2941170 a + 646896\) , \( -967645656 a^{3} - 800385364 a^{2} + 2408187431 a + 529587766\bigr] \)
145.1-d3 \( \bigl[a + 1\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a + 1\) , \( a^{3} + 2 a^{2} - 4 a - 1\bigr] \)
145.1-d4 \( \bigl[a + 1\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - 15 a^{2} + 19 a + 6\) , \( -19 a^{3} + 48 a^{2} - 22 a - 7\bigr] \)

Rank

Rank not yet determined.

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