Elliptic curves over $\Q$ of conductor 312

Results (16 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
312.a1	312d3	312.a	312d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \)	\( 2^{10} \cdot 3^{8} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.57	2B	$624$	$192$	$3$	$1$	$1$		$1$	$128$	$0.302834$	$3044193988/85293$	$0.95679$	$5.00922$	$[0, -1, 0, -304, -1892]$	\(y^2=x^3-x^2-304x-1892\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 26.6.0.b.1, 48.48.0-48.i.1.8, $\ldots$	$[]$
312.a2	312d2	312.a	312d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \)	\( 2^{8} \cdot 3^{4} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.7	2Cs	$312$	$192$	$3$	$1$	$1$		$3$	$64$	$-0.043740$	$37642192/13689$	$0.91195$	$4.00293$	$[0, -1, 0, -44, 84]$	\(y^2=x^3-x^2-44x+84\)	2.6.0.a.1, 4.24.0-4.a.1.1, 24.48.0-24.k.1.1, 52.48.0-52.b.1.1, 104.96.0.?, $\ldots$	$[]$
312.a3	312d1	312.a	312d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \)	\( 2^{4} \cdot 3^{2} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.47	2B	$624$	$192$	$3$	$1$	$1$		$3$	$32$	$-0.390314$	$420616192/117$	$0.96408$	$3.94042$	$[0, -1, 0, -39, 108]$	\(y^2=x^3-x^2-39x+108\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 26.6.0.b.1, 48.48.0-48.i.1.4, $\ldots$	$[]$
312.a4	312d4	312.a	312d	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \)	\( - 2^{10} \cdot 3^{2} \cdot 13^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.11	2B	$624$	$192$	$3$	$1$	$1$		$3$	$128$	$0.302834$	$269676572/257049$	$0.96683$	$4.58718$	$[0, -1, 0, 136, 444]$	\(y^2=x^3-x^2+136x+444\)	2.3.0.a.1, 4.24.0-4.d.1.1, 12.48.0-12.e.1.2, 104.48.0.?, 208.96.0.?, $\ldots$	$[]$
312.b1	312b1	312.b	312b	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \)	\( 2^{4} \cdot 3^{2} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.381084012$	$1$		$9$	$16$	$-0.677175$	$256000/117$	$0.88864$	$2.65114$	$[0, -1, 0, -3, 0]$	\(y^2=x^3-x^2-3x\)	2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.?	$[(3, 3)]$
312.b2	312b2	312.b	312b	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \)	\( - 2^{8} \cdot 3 \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.762168024$	$1$		$5$	$32$	$-0.330601$	$686000/507$	$0.86569$	$3.30555$	$[0, -1, 0, 12, -12]$	\(y^2=x^3-x^2+12x-12\)	2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.?	$[(2, 4)]$
312.c1	312e1	312.c	312e	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \)	\( 2^{4} \cdot 3^{10} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$240$	$0.536386$	$1909913257984/129730653$	$1.03790$	$5.40670$	$[0, -1, 0, -651, 6228]$	\(y^2=x^3-x^2-651x+6228\)	2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.?	$[]$
312.c2	312e2	312.c	312e	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \)	\( - 2^{8} \cdot 3^{5} \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$480$	$0.882959$	$77366117936/1172914587$	$1.04122$	$5.89304$	$[0, -1, 0, 564, 25668]$	\(y^2=x^3-x^2+564x+25668\)	2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.?	$[]$
312.d1	312f2	312.d	312f	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \)	\( 2^{8} \cdot 3^{6} \cdot 13 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.103814520$	$1$		$17$	$96$	$-0.038467$	$94875856/9477$	$0.90366$	$4.16389$	$[0, 1, 0, -60, 144]$	\(y^2=x^3+x^2-60x+144\)	2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.?	$[(6, 6)]$
312.d2	312f1	312.d	312f	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \)	\( - 2^{4} \cdot 3^{3} \cdot 13^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.207629040$	$1$		$11$	$48$	$-0.385041$	$702464/4563$	$0.96739$	$3.23171$	$[0, 1, 0, 5, 14]$	\(y^2=x^3+x^2+5x+14\)	2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.?	$[(-1, 3)]$
312.e1	312a2	312.e	312a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \)	\( 2^{8} \cdot 3^{2} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$32$	$-0.213861$	$137842000/117$	$0.90407$	$4.22894$	$[0, 1, 0, -68, -240]$	\(y^2=x^3+x^2-68x-240\)	2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.?	$[]$
312.e2	312a1	312.e	312a	$2$	$2$	\( 2^{3} \cdot 3 \cdot 13 \)	\( - 2^{4} \cdot 3 \cdot 13^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$16$	$-0.560434$	$-256000/507$	$0.90091$	$2.91001$	$[0, 1, 0, -3, -6]$	\(y^2=x^3+x^2-3x-6\)	2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.?	$[]$
312.f1	312c3	312.f	312c	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \)	\( 2^{10} \cdot 3 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$312$	$48$	$0$	$1$	$4$	$2$	$1$	$64$	$0.203125$	$62275269892/39$	$1.05219$	$5.53479$	$[0, 1, 0, -832, -9520]$	\(y^2=x^3+x^2-832x-9520\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.z.1.4, $\ldots$	$[]$
312.f2	312c2	312.f	312c	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \)	\( 2^{8} \cdot 3^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$156$	$48$	$0$	$1$	$1$		$3$	$32$	$-0.143448$	$61918288/1521$	$0.98715$	$4.08959$	$[0, 1, 0, -52, -160]$	\(y^2=x^3+x^2-52x-160\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 52.24.0-52.b.1.1, 156.48.0.?	$[]$
312.f3	312c1	312.f	312c	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \)	\( 2^{4} \cdot 3^{4} \cdot 13 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$312$	$48$	$0$	$1$	$1$		$3$	$16$	$-0.490022$	$2725888/1053$	$0.92420$	$3.06301$	$[0, 1, 0, -7, 2]$	\(y^2=x^3+x^2-7x+2\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 26.6.0.b.1, 52.24.0-52.g.1.2, $\ldots$	$[]$
312.f4	312c4	312.f	312c	$4$	$4$	\( 2^{3} \cdot 3 \cdot 13 \)	\( - 2^{10} \cdot 3 \cdot 13^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$312$	$48$	$0$	$1$	$1$		$1$	$64$	$0.203125$	$48668/85683$	$1.07537$	$4.48272$	$[0, 1, 0, 8, -448]$	\(y^2=x^3+x^2+8x-448\)	2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 12.24.0-12.g.1.1, 104.24.0.?, $\ldots$	$[]$