Properties

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

Isogeny class 145.3-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
145.3-a1 \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 767 a^{3} + 261 a^{2} - 2731 a - 600\) , \( 14439 a^{3} + 4899 a^{2} - 51204 a - 10817\bigr] \)
145.3-a2 \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( -188 a^{3} - 529 a^{2} - 346 a - 90\) , \( 35387 a^{3} + 22219 a^{2} - 103338 a - 22206\bigr] \)
145.3-a3 \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 42 a^{3} + 21 a^{2} - 151 a - 60\) , \( -142 a^{3} - 72 a^{2} + 501 a + 193\bigr] \)
145.3-a4 \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 7 a^{3} - 19 a^{2} - 86 a - 45\) , \( 353 a^{3} + 222 a^{2} - 980 a - 125\bigr] \)
145.3-a5 \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 47 a^{3} + 16 a^{2} - 166 a - 35\) , \( 275 a^{3} + 93 a^{2} - 975 a - 206\bigr] \)
145.3-a6 \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 47 a^{3} + 11 a^{2} - 161 a - 30\) , \( 283 a^{3} + 87 a^{2} - 990 a - 215\bigr] \)
145.3-a7 \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 2 a^{3} + a^{2} - 6 a\) , \( 7 a^{3} + 3 a^{2} - 24 a - 6\bigr] \)
145.3-a8 \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( -358 a^{3} - 149 a^{2} + 1214 a + 240\) , \( -301 a^{3} - 19 a^{2} + 1354 a + 404\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 12 & 6 & 2 & 4 & 4 & 12 \\ 3 & 1 & 4 & 2 & 6 & 12 & 12 & 4 \\ 12 & 4 & 1 & 2 & 6 & 12 & 3 & 4 \\ 6 & 2 & 2 & 1 & 3 & 6 & 6 & 2 \\ 2 & 6 & 6 & 3 & 1 & 2 & 2 & 6 \\ 4 & 12 & 12 & 6 & 2 & 1 & 4 & 3 \\ 4 & 12 & 3 & 6 & 2 & 4 & 1 & 12 \\ 12 & 4 & 4 & 2 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph