Elliptic curves over $\Q$ of conductor 345

Results (12 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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images
345.a1	345f1	345.a	345f	$1$	$1$	\( 3 \cdot 5 \cdot 23 \)	\( - 3^{8} \cdot 5^{3} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$230$	$2$	$0$	$0.021448892$	$1$		$18$	$192$	$0.122786$	$-111701610496/18862875$	$[0, 1, 1, -100, 406]$	\(y^2+y=x^3+x^2-100x+406\)	230.2.0.?
345.b1	345d3	345.b	345d	$4$	$4$	\( 3 \cdot 5 \cdot 23 \)	\( 3 \cdot 5^{2} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$552$	$48$	$0$	$1$	$1$		$0$	$160$	$0.278322$	$7679186557489/20988075$	$[1, 0, 0, -411, -3234]$	\(y^2+xy=x^3-411x-3234\)	2.3.0.a.1, 4.12.0-4.c.1.2, 12.24.0-12.h.1.1, 184.24.0.?, 552.48.0.?
345.b2	345d4	345.b	345d	$4$	$4$	\( 3 \cdot 5 \cdot 23 \)	\( 3 \cdot 5^{8} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$552$	$48$	$0$	$1$	$1$		$0$	$160$	$0.278322$	$6117442271569/26953125$	$[1, 0, 0, -381, 2820]$	\(y^2+xy=x^3-381x+2820\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.12, $\ldots$
345.b3	345d2	345.b	345d	$4$	$4$	\( 3 \cdot 5 \cdot 23 \)	\( 3^{2} \cdot 5^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$276$	$48$	$0$	$1$	$1$		$2$	$80$	$-0.068251$	$5168743489/2975625$	$[1, 0, 0, -36, -9]$	\(y^2+xy=x^3-36x-9\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.2, 92.24.0.?, 276.48.0.?
345.b4	345d1	345.b	345d	$4$	$4$	\( 3 \cdot 5 \cdot 23 \)	\( - 3^{4} \cdot 5^{2} \cdot 23 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$552$	$48$	$0$	$1$	$1$		$3$	$40$	$-0.414825$	$80062991/46575$	$[1, 0, 0, 9, 0]$	\(y^2+xy=x^3+9x\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 46.6.0.a.1, 92.24.0.?, $\ldots$
345.c1	345a1	345.c	345a	$1$	$1$	\( 3 \cdot 5 \cdot 23 \)	\( - 3^{2} \cdot 5^{5} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$230$	$2$	$0$	$1$	$1$		$0$	$80$	$0.251885$	$-43258336804864/646875$	$[0, -1, 1, -731, -7369]$	\(y^2+y=x^3-x^2-731x-7369\)	230.2.0.?
345.d1	345b1	345.d	345b	$1$	$1$	\( 3 \cdot 5 \cdot 23 \)	\( - 3^{2} \cdot 5 \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$230$	$2$	$0$	$0.185735023$	$1$		$6$	$16$	$-0.736079$	$-262144/1035$	$[0, 1, 1, -1, 1]$	\(y^2+y=x^3+x^2-x+1\)	230.2.0.?
345.e1	345c4	345.e	345c	$4$	$4$	\( 3 \cdot 5 \cdot 23 \)	\( 3^{5} \cdot 5^{12} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$2760$	$48$	$0$	$1$	$1$		$0$	$1200$	$1.286274$	$3026030815665395929/1364501953125$	$[1, 0, 1, -30134, 2010071]$	\(y^2+xy+y=x^3-30134x+2010071\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0-4.c.1.5, 92.12.0.?, $\ldots$
345.e2	345c3	345.e	345c	$4$	$4$	\( 3 \cdot 5 \cdot 23 \)	\( 3^{20} \cdot 5^{3} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$2760$	$48$	$0$	$1$	$1$		$0$	$1200$	$1.286274$	$502552788401502649/10024505152875$	$[1, 0, 1, -16564, -807613]$	\(y^2+xy+y=x^3-16564x-807613\)	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0-4.c.1.3, 92.12.0.?, $\ldots$
345.e3	345c2	345.e	345c	$4$	$4$	\( 3 \cdot 5 \cdot 23 \)	\( 3^{10} \cdot 5^{6} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$1380$	$48$	$0$	$1$	$1$		$2$	$600$	$0.939700$	$1159246431432649/488076890625$	$[1, 0, 1, -2189, 20387]$	\(y^2+xy+y=x^3-2189x+20387\)	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0-2.a.1.1, 60.24.0-60.b.1.3, 92.12.0.?, $\ldots$
345.e4	345c1	345.e	345c	$4$	$4$	\( 3 \cdot 5 \cdot 23 \)	\( - 3^{5} \cdot 5^{3} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$2760$	$48$	$0$	$1$	$1$		$1$	$300$	$0.593126$	$10519294081031/8500170375$	$[1, 0, 1, 456, 2401]$	\(y^2+xy+y=x^3+456x+2401\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 20.12.0-4.c.1.2, 30.6.0.a.1, $\ldots$
345.f1	345e1	345.f	345e	$1$	$1$	\( 3 \cdot 5 \cdot 23 \)	\( - 3^{4} \cdot 5 \cdot 23^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$230$	$2$	$0$	$1$	$1$		$0$	$96$	$-0.030843$	$2887553024/4927635$	$[0, -1, 1, 30, -97]$	\(y^2+y=x^3-x^2+30x-97\)	230.2.0.?