Elliptic curves over \(\Q(\zeta_{15})^+\) of conductor 144.1

Results (8 matches)

 

Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
144.1-a1	144.1-a	$4$	$10$	\(\Q(\zeta_{15})^+\)	$4$	$[4, 0]$	144.1	\( 2^{4} \cdot 3^{2} \)	\( 2^{40} \cdot 3^{20} \)	$5.57841$	$(-a^3+a^2+3a-2), (2)$	0	$\Z/10\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 5$	2B, 5B.1.1[2]	$1$	\( 2^{2} \cdot 5^{2} \)	$1$	$48.99321078$	1.460695330	\( -\frac{19465109}{248832} \)	\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - 3 a\) , \( -9953 a^{3} - 8233 a^{2} + 24770 a + 5451\) , \( 3556183 a^{3} + 2941287 a^{2} - 8850732 a - 1946362\bigr] \)	${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-9953a^{3}-8233a^{2}+24770a+5451\right){x}+3556183a^{3}+2941287a^{2}-8850732a-1946362$
144.1-a2	144.1-a	$4$	$10$	\(\Q(\zeta_{15})^+\)	$4$	$[4, 0]$	144.1	\( 2^{4} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{40} \)	$5.57841$	$(-a^3+a^2+3a-2), (2)$	0	$\Z/10\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 5$	2B, 5B.1.1[2]	$1$	\( 2^{2} \cdot 5^{2} \)	$1$	$48.99321078$	1.460695330	\( \frac{502270291349}{1889568} \)	\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - 3 a\) , \( -294113 a^{3} - 243273 a^{2} + 731970 a + 160971\) , \( 118524887 a^{3} + 98030887 a^{2} - 294988204 a - 64870810\bigr] \)	${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-294113a^{3}-243273a^{2}+731970a+160971\right){x}+118524887a^{3}+98030887a^{2}-294988204a-64870810$
144.1-a3	144.1-a	$4$	$10$	\(\Q(\zeta_{15})^+\)	$4$	$[4, 0]$	144.1	\( 2^{4} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{4} \)	$5.57841$	$(-a^3+a^2+3a-2), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 5$	2B, 5B.1.4[2]	$1$	\( 2^{2} \)	$1$	$48.99321078$	1.460695330	\( -\frac{24389}{12} \)	\( \bigl[a^{2} - 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 2 a\) , \( -a^{3} - 3 a^{2} + 2 a + 6\) , \( -4 a^{2} + 3 a + 3\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(-a^{3}-3a^{2}+2a+6\right){x}-4a^{2}+3a+3$
144.1-a4	144.1-a	$4$	$10$	\(\Q(\zeta_{15})^+\)	$4$	$[4, 0]$	144.1	\( 2^{4} \cdot 3^{2} \)	\( 2^{4} \cdot 3^{8} \)	$5.57841$	$(-a^3+a^2+3a-2), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 5$	2B, 5B.1.4[2]	$1$	\( 2^{2} \)	$1$	$48.99321078$	1.460695330	\( \frac{131872229}{18} \)	\( \bigl[a^{2} - 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 2 a\) , \( -11 a^{3} - 33 a^{2} + 52 a + 16\) , \( -20 a^{3} - 134 a^{2} + 183 a + 43\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(-11a^{3}-33a^{2}+52a+16\right){x}-20a^{3}-134a^{2}+183a+43$
144.1-b1	144.1-b	$4$	$10$	\(\Q(\zeta_{15})^+\)	$4$	$[4, 0]$	144.1	\( 2^{4} \cdot 3^{2} \)	\( 2^{40} \cdot 3^{20} \)	$5.57841$	$(-a^3+a^2+3a-2), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 5$	2B, 5B.1.4[2]	$1$	\( 2^{2} \cdot 5 \)	$0.686404979$	$3.139930371$	1.285151056	\( -\frac{19465109}{248832} \)	\( \bigl[a^{2} - 1\) , \( -1\) , \( a^{3} - 3 a + 1\) , \( -4355 a^{3} - 3604 a^{2} + 10834 a + 2383\) , \( -1033349 a^{3} - 854686 a^{2} + 2571802 a + 565564\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}-{x}^{2}+\left(-4355a^{3}-3604a^{2}+10834a+2383\right){x}-1033349a^{3}-854686a^{2}+2571802a+565564$
144.1-b2	144.1-b	$4$	$10$	\(\Q(\zeta_{15})^+\)	$4$	$[4, 0]$	144.1	\( 2^{4} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{40} \)	$5.57841$	$(-a^3+a^2+3a-2), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 5$	2B, 5B.1.4[2]	$1$	\( 2 \cdot 5 \)	$1.372809958$	$3.139930371$	1.285151056	\( \frac{502270291349}{1889568} \)	\( \bigl[a^{2} - 1\) , \( -1\) , \( a^{3} - 3 a + 1\) , \( -128675 a^{3} - 106484 a^{2} + 320114 a + 70383\) , \( -34429829 a^{3} - 28477022 a^{2} + 85689050 a + 18843868\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}-{x}^{2}+\left(-128675a^{3}-106484a^{2}+320114a+70383\right){x}-34429829a^{3}-28477022a^{2}+85689050a+18843868$
144.1-b3	144.1-b	$4$	$10$	\(\Q(\zeta_{15})^+\)	$4$	$[4, 0]$	144.1	\( 2^{4} \cdot 3^{2} \)	\( 2^{4} \cdot 3^{8} \)	$5.57841$	$(-a^3+a^2+3a-2), (2)$	$1$	$\Z/10\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 5$	2B, 5B.1.1[2]	$1$	\( 2 \)	$0.274561991$	$1962.456482$	1.285151056	\( \frac{131872229}{18} \)	\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 3 a\) , \( -10 a^{3} + 30 a - 21\) , \( 31 a^{3} - 93 a + 51\bigr] \)	${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(-10a^{3}+30a-21\right){x}+31a^{3}-93a+51$
144.1-b4	144.1-b	$4$	$10$	\(\Q(\zeta_{15})^+\)	$4$	$[4, 0]$	144.1	\( 2^{4} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{4} \)	$5.57841$	$(-a^3+a^2+3a-2), (2)$	$1$	$\Z/10\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 5$	2B, 5B.1.1[2]	$1$	\( 2^{2} \)	$0.137280995$	$1962.456482$	1.285151056	\( -\frac{24389}{12} \)	\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 3 a\) , \( -1\) , \( a^{3} - 3 a + 1\bigr] \)	${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}-{x}+a^{3}-3a+1$

 

  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.