Properties

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

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

Curve label Weierstrass Coefficients
145.3-e1 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a\) , \( -791 a^{3} + 688 a^{2} + 3761 a - 4369\) , \( -28142 a^{3} + 39690 a^{2} + 87295 a - 120457\bigr] \)
145.3-e2 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a\) , \( -56 a^{3} + 38 a^{2} + 251 a - 269\) , \( -434 a^{3} + 563 a^{2} + 1276 a - 1676\bigr] \)
145.3-e3 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a\) , \( -6 a^{3} + 8 a^{2} + 26 a - 34\) , \( 14 a^{3} - 15 a^{2} - 59 a + 72\bigr] \)
145.3-e4 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a\) , \( -121 a^{3} - 132 a^{2} + 341 a + 71\) , \( -2518 a^{3} + 448 a^{2} + 7457 a - 4747\bigr] \)

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