Elliptic curves over $\Q$ of conductor 978

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Results (10 matches)

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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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
978.a1	978d1	978.a	978d	$1$	$1$	\( 2 \cdot 3 \cdot 163 \)	\( - 2^{5} \cdot 3^{13} \cdot 163 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3912$	$2$	$0$	$1$	$1$		$0$	$1560$	$0.591431$	$10588578877079/8315988768$	$0.96598$	$4.35564$		$[1, 1, 0, 458, -2060]$	\(y^2+xy=x^3+x^2+458x-2060\)	3912.2.0.?	$[ ]$	$1$
978.b1	978c1	978.b	978c	$1$	$1$	\( 2 \cdot 3 \cdot 163 \)	\( 2^{13} \cdot 3^{26} \cdot 163 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1304$	$2$	$0$	$1$	$1$		$0$	$40560$	$2.426010$	$1158608829852384342018553/3394143273104400384$	$1.04433$	$8.04723$		$[1, 1, 0, -2188119, -1243572651]$	\(y^2+xy=x^3+x^2-2188119x-1243572651\)	1304.2.0.?	$[ ]$	$1$
978.c1	978a1	978.c	978a	$1$	$1$	\( 2 \cdot 3 \cdot 163 \)	\( - 2^{19} \cdot 3^{5} \cdot 163 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$3912$	$2$	$0$	$1$	$1$		$0$	$2280$	$1.198662$	$-5911920517162731625/20766523392$	$1.00742$	$6.27746$		$[1, 1, 0, -37670, 2798484]$	\(y^2+xy=x^3+x^2-37670x+2798484\)	3912.2.0.?	$[ ]$	$1$
978.d1	978b1	978.d	978b	$2$	$2$	\( 2 \cdot 3 \cdot 163 \)	\( 2^{2} \cdot 3 \cdot 163 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.4	2B	$3912$	$12$	$0$	$1$	$1$		$1$	$60$	$-0.577857$	$95443993/1956$	$0.82844$	$2.66851$		$[1, 1, 0, -9, -15]$	\(y^2+xy=x^3+x^2-9x-15\)	2.3.0.a.1, 8.6.0.d.1, 978.6.0.?, 3912.12.0.?	$[ ]$	$1$
978.d2	978b2	978.d	978b	$2$	$2$	\( 2 \cdot 3 \cdot 163 \)	\( - 2 \cdot 3^{2} \cdot 163^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.6.0.5	2B	$3912$	$12$	$0$	$1$	$1$		$0$	$120$	$-0.231284$	$12167/478242$	$1.01209$	$2.98200$		$[1, 1, 0, 1, -33]$	\(y^2+xy=x^3+x^2+x-33\)	2.3.0.a.1, 8.6.0.a.1, 1956.6.0.?, 3912.12.0.?	$[ ]$	$1$
978.e1	978e1	978.e	978e	$1$	$1$	\( 2 \cdot 3 \cdot 163 \)	\( 2 \cdot 3^{2} \cdot 163 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1304$	$2$	$0$	$0.229405419$	$1$		$4$	$80$	$-0.628207$	$10218313/2934$	$0.80729$	$2.34401$		$[1, 0, 1, -5, 2]$	\(y^2+xy+y=x^3-5x+2\)	1304.2.0.?	$[(0, 1)]$	$1$
978.f1	978f1	978.f	978f	$1$	$1$	\( 2 \cdot 3 \cdot 163 \)	\( 2^{11} \cdot 3^{2} \cdot 163 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1304$	$2$	$0$	$0.050334838$	$1$		$14$	$176$	$0.044607$	$196021690129/3004416$	$0.91105$	$3.77626$		$[1, 1, 1, -121, 455]$	\(y^2+xy+y=x^3+x^2-121x+455\)	1304.2.0.?	$[(-1, 24)]$	$1$
978.g1	978g1	978.g	978g	$1$	$1$	\( 2 \cdot 3 \cdot 163 \)	\( 2^{7} \cdot 3^{8} \cdot 163 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$1304$	$2$	$0$	$0.036076195$	$1$		$16$	$448$	$0.252354$	$254478514753/136888704$	$0.95692$	$3.81417$		$[1, 0, 0, -132, 144]$	\(y^2+xy=x^3-132x+144\)	1304.2.0.?	$[(-6, 30)]$	$1$
978.h1	978h1	978.h	978h	$2$	$3$	\( 2 \cdot 3 \cdot 163 \)	\( - 2^{3} \cdot 3^{3} \cdot 163 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.1	3B.1.1	$3912$	$16$	$0$	$1$	$1$		$2$	$72$	$-0.445658$	$-3048625/35208$	$0.86206$	$2.61021$		$[1, 0, 0, -3, 9]$	\(y^2+xy=x^3-3x+9\)	3.8.0-3.a.1.2, 3912.16.0.?	$[ ]$	$1$
978.h2	978h2	978.h	978h	$2$	$3$	\( 2 \cdot 3 \cdot 163 \)	\( - 2 \cdot 3 \cdot 163^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$3$	3.8.0.2	3B.1.2	$3912$	$16$	$0$	$1$	$1$		$0$	$216$	$0.103648$	$2171747375/25984482$	$0.93294$	$3.55502$		$[1, 0, 0, 27, -237]$	\(y^2+xy=x^3+27x-237\)	3.8.0-3.a.1.1, 3912.16.0.?	$[ ]$	$1$

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