Elliptic curves over $\Q$ of conductor 294

Results (18 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
294.a1	294e2	294.a	294e	$2$	$3$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2^{15} \cdot 3 \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$168$	$16$	$0$	$1$	$1$		$0$	$1260$	$1.419874$	$-16591834777/98304$	$1.06741$	$7.56591$	$[1, 1, 0, -34864, 2503936]$	\(y^2+xy=x^3+x^2-34864x+2503936\)	3.4.0.a.1, 21.8.0-3.a.1.2, 24.8.0.d.1, 168.16.0.?	$[]$
294.a2	294e1	294.a	294e	$2$	$3$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2^{5} \cdot 3^{3} \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$168$	$16$	$0$	$1$	$1$		$0$	$420$	$0.870567$	$596183/864$	$1.03569$	$5.83535$	$[1, 1, 0, 1151, 18901]$	\(y^2+xy=x^3+x^2+1151x+18901\)	3.4.0.a.1, 21.8.0-3.a.1.1, 24.8.0.d.1, 168.16.0.?	$[]$
294.b1	294f2	294.b	294f	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \)	\( 2^{2} \cdot 3^{8} \cdot 7^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.204	2B	$56$	$96$	$1$	$1$	$1$		$0$	$896$	$1.082436$	$838561807/26244$	$1.03462$	$6.69655$	$[1, 1, 0, -6738, -209880]$	\(y^2+xy=x^3+x^2-6738x-209880\)	2.3.0.a.1, 4.12.0.f.1, 8.48.0.q.2, 28.24.0.i.1, 56.96.1.cq.1	$[]$
294.b2	294f1	294.b	294f	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2^{4} \cdot 3^{4} \cdot 7^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.203	2B	$56$	$96$	$1$	$1$	$1$		$1$	$448$	$0.735863$	$4913/1296$	$1.13279$	$5.65361$	$[1, 1, 0, 122, -10940]$	\(y^2+xy=x^3+x^2+122x-10940\)	2.3.0.a.1, 4.12.0.f.1, 8.48.0.q.1, 14.6.0.b.1, 28.24.0.g.1, $\ldots$	$[]$
294.c1	294g2	294.c	294g	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \)	\( 2^{2} \cdot 3^{8} \cdot 7^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.204	2B	$56$	$96$	$1$	$0.067253936$	$1$		$20$	$128$	$0.109481$	$838561807/26244$	$1.03462$	$4.64231$	$[1, 0, 1, -138, 592]$	\(y^2+xy+y=x^3-138x+592\)	2.3.0.a.1, 4.12.0.f.1, 8.48.0.q.2, 28.24.0.i.1, 56.96.1.cq.1	$[(-1, 27)]$
294.c2	294g1	294.c	294g	$2$	$2$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2^{4} \cdot 3^{4} \cdot 7^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.203	2B	$56$	$96$	$1$	$0.134507872$	$1$		$15$	$64$	$-0.237092$	$4913/1296$	$1.13279$	$3.59937$	$[1, 0, 1, 2, 32]$	\(y^2+xy+y=x^3+2x+32\)	2.3.0.a.1, 4.12.0.f.1, 8.48.0.q.1, 14.6.0.b.1, 28.24.0.g.1, $\ldots$	$[(1, 5)]$
294.d1	294d2	294.d	294d	$2$	$3$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2^{15} \cdot 3 \cdot 7^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$24$	$16$	$0$	$1$	$1$		$0$	$180$	$0.446919$	$-16591834777/98304$	$1.06741$	$5.51167$	$[1, 0, 1, -712, -7402]$	\(y^2+xy+y=x^3-712x-7402\)	3.8.0-3.a.1.1, 24.16.0-24.d.1.7	$[]$
294.d2	294d1	294.d	294d	$2$	$3$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2^{5} \cdot 3^{3} \cdot 7^{4} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$24$	$16$	$0$	$1$	$1$		$2$	$60$	$-0.102387$	$596183/864$	$1.03569$	$3.78111$	$[1, 0, 1, 23, -52]$	\(y^2+xy+y=x^3+23x-52\)	3.8.0-3.a.1.2, 24.16.0-24.d.1.8	$[]$
294.e1	294a2	294.e	294a	$2$	$7$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2^{7} \cdot 3^{7} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.48.0.4	7B.1.6	$168$	$96$	$2$	$1$	$1$		$0$	$588$	$1.107431$	$-6329617441/279936$	$1.03234$	$6.72278$	$[1, 1, 1, -6910, -232261]$	\(y^2+xy+y=x^3+x^2-6910x-232261\)	7.48.0-7.a.1.1, 24.2.0.b.1, 168.96.2.?	$[]$
294.e2	294a1	294.e	294a	$2$	$7$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2 \cdot 3 \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.48.0.2	7B.1.4	$168$	$96$	$2$	$1$	$1$		$0$	$84$	$0.134477$	$-2401/6$	$1.11692$	$4.40252$	$[1, 1, 1, -50, 293]$	\(y^2+xy+y=x^3+x^2-50x+293\)	7.48.0-7.a.2.1, 24.2.0.b.1, 168.96.2.?	$[]$
294.f1	294b2	294.f	294b	$2$	$7$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2^{7} \cdot 3^{7} \cdot 7^{2} \)	$0$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$			$7$	7.48.0.1	7B.1.1	$168$	$96$	$2$	$1$	$1$		$6$	$84$	$0.134477$	$-6329617441/279936$	$1.03234$	$4.66853$	$[1, 0, 0, -141, 657]$	\(y^2+xy=x^3-141x+657\)	7.48.0-7.a.1.2, 24.2.0.b.1, 168.96.2.?	$[]$
294.f2	294b1	294.f	294b	$2$	$7$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2 \cdot 3 \cdot 7^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.48.0.5	7B.1.3	$168$	$96$	$2$	$1$	$1$		$0$	$12$	$-0.838478$	$-2401/6$	$1.11692$	$2.34827$	$[1, 0, 0, -1, -1]$	\(y^2+xy=x^3-x-1\)	7.48.0-7.a.2.2, 24.2.0.b.1, 168.96.2.?	$[]$
294.g1	294c3	294.g	294c	$6$	$8$	\( 2 \cdot 3 \cdot 7^{2} \)	\( 2^{2} \cdot 3^{2} \cdot 7^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.167	2B	$112$	$192$	$1$	$1$	$4$	$2$	$0$	$768$	$1.162056$	$268498407453697/252$	$1.05727$	$7.89983$	$[1, 0, 0, -65857, -6510547]$	\(y^2+xy=x^3-65857x-6510547\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.6, 16.96.0-16.z.2.5, 28.24.0-28.h.1.1, $\ldots$	$[]$
294.g2	294c5	294.g	294c	$6$	$8$	\( 2 \cdot 3 \cdot 7^{2} \)	\( 2 \cdot 3^{4} \cdot 7^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.245	2B	$112$	$192$	$1$	$1$	$1$		$0$	$1536$	$1.508631$	$84448510979617/933897762$	$1.05309$	$7.69632$	$[1, 0, 0, -44787, 3609423]$	\(y^2+xy=x^3-44787x+3609423\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0.p.1, 16.96.0-8.p.1.2, 28.12.0-4.c.1.1, $\ldots$	$[]$
294.g3	294c4	294.g	294c	$6$	$8$	\( 2 \cdot 3 \cdot 7^{2} \)	\( 2^{2} \cdot 3^{8} \cdot 7^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.96.0.110	2Cs	$56$	$192$	$1$	$1$	$1$		$2$	$768$	$1.162056$	$124475734657/63011844$	$1.06499$	$6.54919$	$[1, 0, 0, -5097, -49995]$	\(y^2+xy=x^3-5097x-49995\)	2.6.0.a.1, 4.12.0.b.1, 8.96.0-8.f.1.2, 28.24.0-4.b.1.1, 56.192.1-56.bp.2.1	$[]$
294.g4	294c2	294.g	294c	$6$	$8$	\( 2 \cdot 3 \cdot 7^{2} \)	\( 2^{4} \cdot 3^{4} \cdot 7^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.96.0.20	2Cs	$56$	$192$	$1$	$1$	$1$		$2$	$384$	$0.815483$	$65597103937/63504$	$1.01692$	$6.43648$	$[1, 0, 0, -4117, -101935]$	\(y^2+xy=x^3-4117x-101935\)	2.6.0.a.1, 4.24.0-4.b.1.2, 8.96.0-8.i.1.5, 28.48.0-28.c.1.4, 56.192.1-56.by.1.2	$[]$
294.g5	294c1	294.g	294c	$6$	$8$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2^{8} \cdot 3^{2} \cdot 7^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.118	2B	$112$	$192$	$1$	$1$	$1$		$3$	$192$	$0.468909$	$-7189057/16128$	$0.98224$	$5.11086$	$[1, 0, 0, -197, -2367]$	\(y^2+xy=x^3-197x-2367\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.8, 14.6.0.b.1, 16.96.0-16.z.1.7, $\ldots$	$[]$
294.g6	294c6	294.g	294c	$6$	$8$	\( 2 \cdot 3 \cdot 7^{2} \)	\( - 2 \cdot 3^{16} \cdot 7^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.213	2B	$112$	$192$	$1$	$1$	$1$		$0$	$1536$	$1.508631$	$6359387729183/4218578658$	$1.08314$	$7.24128$	$[1, 0, 0, 18913, -381333]$	\(y^2+xy=x^3+18913x-381333\)	2.3.0.a.1, 4.6.0.c.1, 8.48.0-8.k.1.3, 16.96.0-16.e.1.7, 28.12.0-4.c.1.1, $\ldots$	$[]$