Elliptic curves over $\Q$ of conductor 1005

Results (4 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
1005.a1	1005b2	1005.a	1005b	$2$	$3$	\( 3 \cdot 5 \cdot 67 \)	\( - 3^{4} \cdot 5^{6} \cdot 67^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$402$	$16$	$0$	$0.312315735$	$1$		$4$	$1440$	$0.955898$	$-2989967081734144/380653171875$	$1.01643$	$5.18360$	$[0, 1, 1, -3001, -70904]$	\(y^2+y=x^3+x^2-3001x-70904\)	3.8.0-3.a.1.1, 134.2.0.?, 402.16.0.?	$[(542, 12562)]$
1005.a2	1005b1	1005.a	1005b	$2$	$3$	\( 3 \cdot 5 \cdot 67 \)	\( - 3^{12} \cdot 5^{2} \cdot 67 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$402$	$16$	$0$	$0.936947207$	$1$		$8$	$480$	$0.406592$	$1503484706816/890163675$	$1.04611$	$4.05610$	$[0, 1, 1, 239, 295]$	\(y^2+y=x^3+x^2+239x+295\)	3.8.0-3.a.1.2, 134.2.0.?, 402.16.0.?	$[(-1, 7)]$
1005.b1	1005a1	1005.b	1005a	$2$	$2$	\( 3 \cdot 5 \cdot 67 \)	\( 3^{5} \cdot 5^{6} \cdot 67 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$1$	$360$	$0.353420$	$2912566550041/254390625$	$0.91283$	$4.15176$	$[1, 1, 0, -297, -1944]$	\(y^2+xy=x^3+x^2-297x-1944\)	2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.?	$[]$
1005.b2	1005a2	1005.b	1005a	$2$	$2$	\( 3 \cdot 5 \cdot 67 \)	\( - 3^{10} \cdot 5^{3} \cdot 67^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.3.0.1	2B	$4020$	$12$	$0$	$1$	$1$		$0$	$720$	$0.699994$	$3883959939959/33133870125$	$0.95785$	$4.57247$	$[1, 1, 0, 328, -8319]$	\(y^2+xy=x^3+x^2+328x-8319\)	2.3.0.a.1, 20.6.0.a.1, 804.6.0.?, 4020.12.0.?	$[]$