Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-145.3-b
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-b over \(\Q(\zeta_{15})^+\)

Isogeny class 145.3-b contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
145.3-b1 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - 2\) , \( -233588 a^{3} - 193414 a^{2} + 580871 a + 127682\) , \( 85052980 a^{3} + 70349831 a^{2} - 211675141 a - 46549371\bigr] \)
145.3-b2 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - 2\) , \( -234588 a^{3} - 194044 a^{2} + 583826 a + 128387\) , \( 84635877 a^{3} + 70001639 a^{2} - 210644160 a - 46322722\bigr] \)
145.3-b3 \( \bigl[a^{2} + a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{2} + a - 2\) , \( 5 a^{2} - 5 a - 6\) , \( -3 a^{3} + 2 a^{2} + 4 a - 3\bigr] \)
145.3-b4 \( \bigl[a^{2} + a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{2} + a - 2\) , \( -1\) , \( -2 a^{3} - 2 a^{2} + 6 a\bigr] \)

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