Elliptic curves over $\Q$ of conductor 5408

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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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
5408.a1	5408g1	5408.a	5408g	$1$	$1$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{9} \cdot 13^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$22464$	$1.250874$	$-74088$	$0.92990$	$4.71855$	$[0, 0, 0, -15379, -742586]$	\(y^2=x^3-15379x-742586\)	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[]$
5408.b1	5408m1	5408.b	5408m	$1$	$1$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{9} \cdot 13^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$0.943302495$	$1$		$4$	$1728$	$-0.031601$	$-74088$	$0.92990$	$2.92814$	$[0, 0, 0, -91, -338]$	\(y^2=x^3-91x-338\)	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(13, 26)]$
5408.c1	5408j1	5408.c	5408j	$1$	$1$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{12} \cdot 13^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$104$	$4$	$0$	$1$	$1$		$0$	$17472$	$1.573086$	$-10816$	$0.83745$	$5.04957$	$[0, 1, 0, -38081, 3067663]$	\(y^2=x^3+x^2-38081x+3067663\)	4.2.0.a.1, 104.4.0.?	$[]$
5408.d1	5408d1	5408.d	5408d	$1$	$1$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{12} \cdot 13^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.4.0.2		$8$	$4$	$0$	$0.125541278$	$1$		$8$	$1344$	$0.290612$	$-10816$	$0.83745$	$3.25916$	$[0, 1, 0, -225, 1327]$	\(y^2=x^3+x^2-225x+1327\)	4.2.0.a.1, 8.4.0-4.a.1.1	$[(-9, 52)]$
5408.e1	5408b1	5408.e	5408b	$1$	$1$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{9} \cdot 13^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$0.871651939$	$1$		$4$	$2688$	$0.695062$	$-8/13$	$0.95359$	$3.68187$	$[0, -1, 0, -56, 8644]$	\(y^2=x^3-x^2-56x+8644\)	104.2.0.?	$[(48, 338)]$
5408.f1	5408k1	5408.f	5408k	$2$	$2$	\( 2^{5} \cdot 13^{2} \)	\( 2^{6} \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$3.583020519$	$1$		$3$	$6240$	$0.959753$	$1728$		$4.03672$	$[0, 0, 0, -2197, 0]$	\(y^2=x^3-2197x\)		$[(-9, 138)]$
5408.f2	5408k2	5408.f	5408k	$2$	$2$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{12} \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$7.166041039$	$1$		$1$	$12480$	$1.306326$	$1728$		$4.52055$	$[0, 0, 0, 8788, 0]$	\(y^2=x^3+8788x\)		$[(2116/3, 104788/3)]$
5408.g1	5408a2	5408.g	5408a	$4$	$4$	\( 2^{5} \cdot 13^{2} \)	\( 2^{9} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$		✓							$11.66502347$	$1$		$1$	$1920$	$0.665089$	$287496$	$1.17246$	$3.97841$	$[0, 0, 0, -1859, -30758]$	\(y^2=x^3-1859x-30758\)		$[(-224246/95, 8254758/95)]$
5408.g2	5408a3	5408.g	5408a	$4$	$4$	\( 2^{5} \cdot 13^{2} \)	\( 2^{9} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$		✓							$2.916255868$	$1$		$3$	$1920$	$0.665089$	$287496$	$1.17246$	$3.97841$	$[0, 0, 0, -1859, 30758]$	\(y^2=x^3-1859x+30758\)		$[(1, 170)]$
5408.g3	5408a1	5408.g	5408a	$4$	$4$	\( 2^{5} \cdot 13^{2} \)	\( 2^{6} \cdot 13^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.192.9.143	2Cs				$5.832511736$	$1$		$3$	$960$	$0.318515$	$1728$		$3.14151$	$[0, 0, 0, -169, 0]$	\(y^2=x^3-169x\)		$[(-36/5, 1938/5)]$
5408.g4	5408a4	5408.g	5408a	$4$	$4$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{12} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.192.9.178	2B				$2.916255868$	$1$		$3$	$1920$	$0.665089$	$1728$		$3.62535$	$[0, 0, 0, 676, 0]$	\(y^2=x^3+676x\)		$[(468, 10140)]$
5408.h1	5408e1	5408.h	5408e	$2$	$2$	\( 2^{5} \cdot 13^{2} \)	\( 2^{6} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$480$	$-0.322722$	$1728$		$2.24631$	$[0, 0, 0, -13, 0]$	\(y^2=x^3-13x\)		$[]$
5408.h2	5408e2	5408.h	5408e	$2$	$2$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{12} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$960$	$0.023852$	$1728$		$2.73015$	$[0, 0, 0, 52, 0]$	\(y^2=x^3+52x\)		$[]$
5408.i1	5408h1	5408.i	5408h	$1$	$1$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{9} \cdot 13^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$104$	$2$	$0$	$1$	$1$		$0$	$2688$	$0.695062$	$-8/13$	$0.95359$	$3.68187$	$[0, 1, 0, -56, -8644]$	\(y^2=x^3+x^2-56x-8644\)	104.2.0.?	$[]$
5408.j1	5408c1	5408.j	5408c	$1$	$1$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{12} \cdot 13^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$104$	$4$	$0$	$7.249855560$	$1$		$0$	$17472$	$1.573086$	$-10816$	$0.83745$	$5.04957$	$[0, -1, 0, -38081, -3067663]$	\(y^2=x^3-x^2-38081x-3067663\)	4.2.0.a.1, 104.4.0.?	$[(3709/3, 192932/3)]$
5408.k1	5408i1	5408.k	5408i	$1$	$1$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{12} \cdot 13^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.4.0.2		$8$	$4$	$0$	$1$	$1$		$0$	$1344$	$0.290612$	$-10816$	$0.83745$	$3.25916$	$[0, -1, 0, -225, -1327]$	\(y^2=x^3-x^2-225x-1327\)	4.2.0.a.1, 8.4.0-4.a.1.1	$[]$
5408.l1	5408l1	5408.l	5408l	$1$	$1$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{9} \cdot 13^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$3.547654043$	$1$		$0$	$22464$	$1.250874$	$-74088$	$0.92990$	$4.71855$	$[0, 0, 0, -15379, 742586]$	\(y^2=x^3-15379x+742586\)	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(1690/3, 57122/3)]$
5408.m1	5408f1	5408.m	5408f	$1$	$1$	\( 2^{5} \cdot 13^{2} \)	\( - 2^{9} \cdot 13^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$1728$	$-0.031601$	$-74088$	$0.92990$	$2.92814$	$[0, 0, 0, -91, 338]$	\(y^2=x^3-91x+338\)	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[]$

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