Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-145.1-e
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-e over \(\Q(\zeta_{15})^+\)

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

Curve label Weierstrass Coefficients
145.1-e1 \( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( -13 a^{3} + 133 a^{2} + 61 a - 484\) , \( -2909 a^{3} - 665 a^{2} + 8702 a - 2209\bigr] \)
145.1-e2 \( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( -93 a^{3} - 687 a^{2} - 1109 a - 234\) , \( -67039 a^{3} - 41297 a^{2} + 197456 a + 42415\bigr] \)
145.1-e3 \( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( -13 a^{3} - 37 a^{2} - 44 a - 39\) , \( -1144 a^{3} - 675 a^{2} + 3401 a + 673\bigr] \)
145.1-e4 \( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} - 2\) , \( -8 a^{3} - 7 a^{2} + 16 a + 1\) , \( -4 a^{3} + 3 a^{2} + 22 a + 3\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph