Elliptic curve isogeny class 144.1-b over number field \(\Q(\zeta_{15})^+\)

• Base field: \(\Q(\zeta_{15})^+\)
• Label: 4.4.1125.1-144.1-b
• Conductor: 144.1
• Rank: \( 1 \)

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 144.1-b over \(\Q(\zeta_{15})^+\)

Isogeny class 144.1-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
144.1-b1	\( \bigl[a^{2} - 1\) , \( -1\) , \( a^{3} - 3 a + 1\) , \( -4355 a^{3} - 3604 a^{2} + 10834 a + 2383\) , \( -1033349 a^{3} - 854686 a^{2} + 2571802 a + 565564\bigr] \)
144.1-b2	\( \bigl[a^{2} - 1\) , \( -1\) , \( a^{3} - 3 a + 1\) , \( -128675 a^{3} - 106484 a^{2} + 320114 a + 70383\) , \( -34429829 a^{3} - 28477022 a^{2} + 85689050 a + 18843868\bigr] \)
144.1-b3	\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 3 a\) , \( -10 a^{3} + 30 a - 21\) , \( 31 a^{3} - 93 a + 51\bigr] \)
144.1-b4	\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 3 a\) , \( -1\) , \( a^{3} - 3 a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 10 & 5 \\ 2 & 1 & 5 & 10 \\ 10 & 5 & 1 & 2 \\ 5 & 10 & 2 & 1 \end{array}\right)\)

Isogeny graph