Elliptic curves over $\Q$ of conductor 4010

Results (10 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
4010.a1	4010c1	4010.a	4010c	$2$	$3$	\( 2 \cdot 5 \cdot 401 \)	\( - 2^{7} \cdot 5^{6} \cdot 401 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$9624$	$16$	$0$	$1$	$1$		$2$	$11984$	$1.130148$	$-6819665063040893881/802000000$	$0.95240$	$5.22704$	$[1, 0, 1, -39508, 3019218]$	\(y^2+xy+y=x^3-39508x+3019218\)	3.8.0-3.a.1.2, 3208.2.0.?, 9624.16.0.?	$[]$
4010.a2	4010c2	4010.a	4010c	$2$	$3$	\( 2 \cdot 5 \cdot 401 \)	\( - 2^{21} \cdot 5^{2} \cdot 401^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$9624$	$16$	$0$	$1$	$1$		$0$	$35952$	$1.679453$	$-4694045543427107881/3380671990988800$	$1.05420$	$5.27946$	$[1, 0, 1, -34883, 3753918]$	\(y^2+xy+y=x^3-34883x+3753918\)	3.8.0-3.a.1.1, 3208.2.0.?, 9624.16.0.?	$[]$
4010.b1	4010a1	4010.b	4010a	$1$	$1$	\( 2 \cdot 5 \cdot 401 \)	\( - 2^{3} \cdot 5^{2} \cdot 401 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3208$	$2$	$0$	$1.722368778$	$1$		$2$	$528$	$-0.282352$	$-2565726409/80200$	$0.91004$	$2.61773$	$[1, 1, 0, -28, -72]$	\(y^2+xy=x^3+x^2-28x-72\)	3208.2.0.?	$[(9, 18)]$
4010.c1	4010d1	4010.c	4010d	$2$	$2$	\( 2 \cdot 5 \cdot 401 \)	\( 2^{12} \cdot 5^{2} \cdot 401 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.21	2B	$16040$	$48$	$0$	$1.919096695$	$1$		$3$	$1344$	$0.215647$	$729243027001/41062400$	$0.85077$	$3.29237$	$[1, 1, 0, -187, 861]$	\(y^2+xy=x^3+x^2-187x+861\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 802.6.0.?, 1604.12.0.?, $\ldots$	$[(-3, 39)]$
4010.c2	4010d2	4010.c	4010d	$2$	$2$	\( 2 \cdot 5 \cdot 401 \)	\( - 2^{6} \cdot 5^{4} \cdot 401^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.12	2B	$16040$	$48$	$0$	$0.959548347$	$1$		$2$	$2688$	$0.562221$	$257138126279/6432040000$	$0.90587$	$3.61788$	$[1, 1, 0, 133, 3869]$	\(y^2+xy=x^3+x^2+133x+3869\)	2.3.0.a.1, 4.12.0-4.a.1.1, 1604.24.0.?, 16040.48.0.?	$[(-2, 61)]$
4010.d1	4010b1	4010.d	4010b	$1$	$1$	\( 2 \cdot 5 \cdot 401 \)	\( - 2^{5} \cdot 5 \cdot 401 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$16040$	$2$	$0$	$1$	$1$		$0$	$760$	$-0.373981$	$-116930169/64160$	$0.76618$	$2.31952$	$[1, -1, 0, -10, 20]$	\(y^2+xy=x^3-x^2-10x+20\)	16040.2.0.?	$[]$
4010.e1	4010e2	4010.e	4010e	$2$	$5$	\( 2 \cdot 5 \cdot 401 \)	\( - 2^{3} \cdot 5 \cdot 401^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.3	5B.1.2	$16040$	$48$	$1$	$1$	$1$		$0$	$21000$	$1.520990$	$-1524055181537372401/414745664080040$	$0.94999$	$5.09288$	$[1, 1, 1, -23975, -1742523]$	\(y^2+xy+y=x^3+x^2-23975x-1742523\)	5.24.0-5.a.2.2, 16040.48.1.?	$[]$
4010.e2	4010e1	4010.e	4010e	$2$	$5$	\( 2 \cdot 5 \cdot 401 \)	\( - 2^{15} \cdot 5^{5} \cdot 401 \)	$0$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.1	5B.1.1	$16040$	$48$	$1$	$1$	$1$		$4$	$4200$	$0.716271$	$-592915705201/41062400000$	$0.92785$	$3.84514$	$[1, 1, 1, -175, 9717]$	\(y^2+xy+y=x^3+x^2-175x+9717\)	5.24.0-5.a.1.2, 16040.48.1.?	$[]$
4010.f1	4010f2	4010.f	4010f	$2$	$2$	\( 2 \cdot 5 \cdot 401 \)	\( 2^{2} \cdot 5 \cdot 401^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$8020$	$12$	$0$	$1$	$4$	$2$	$0$	$1536$	$0.041856$	$168288035761/3216020$	$0.83602$	$3.11563$	$[1, 1, 1, -115, -515]$	\(y^2+xy+y=x^3+x^2-115x-515\)	2.3.0.a.1, 10.6.0.a.1, 1604.6.0.?, 8020.12.0.?	$[]$
4010.f2	4010f1	4010.f	4010f	$2$	$2$	\( 2 \cdot 5 \cdot 401 \)	\( 2^{4} \cdot 5^{2} \cdot 401 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$8020$	$12$	$0$	$1$	$1$		$1$	$768$	$-0.304718$	$374805361/160400$	$0.78421$	$2.37953$	$[1, 1, 1, -15, 5]$	\(y^2+xy+y=x^3+x^2-15x+5\)	2.3.0.a.1, 20.6.0.c.1, 802.6.0.?, 8020.12.0.?	$[]$