Elliptic curves over $\Q$ of conductor 120

Results (10 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
120.a1	120b3	120.a	120b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \)	\( 2^{11} \cdot 3^{4} \cdot 5 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.7	2B	$120$	$48$	$0$	$1$	$1$		$1$	$32$	$0.069403$	$546718898/405$	$0.99169$	$5.79511$	$[0, 1, 0, -216, -1296]$	\(y^2=x^3+x^2-216x-1296\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 20.12.0-4.c.1.1, 24.24.0-24.y.1.8, $\ldots$	$[]$
120.a2	120b4	120.a	120b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \)	\( 2^{11} \cdot 3 \cdot 5^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.8	2B	$120$	$48$	$0$	$1$	$1$		$1$	$32$	$0.069403$	$136835858/1875$	$0.97925$	$5.50579$	$[0, 1, 0, -136, 560]$	\(y^2=x^3+x^2-136x+560\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 12.12.0-4.c.1.1, 24.24.0-24.s.1.4, $\ldots$	$[]$
120.a3	120b2	120.a	120b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$120$	$48$	$0$	$1$	$1$		$3$	$16$	$-0.277171$	$470596/225$	$1.13245$	$4.17614$	$[0, 1, 0, -16, -16]$	\(y^2=x^3+x^2-16x-16\)	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 20.12.0-2.a.1.1, 24.24.0-24.b.1.2, $\ldots$	$[]$
120.a4	120b1	120.a	120b	$4$	$4$	\( 2^{3} \cdot 3 \cdot 5 \)	\( - 2^{8} \cdot 3 \cdot 5 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.12	2B	$120$	$48$	$0$	$1$	$1$		$1$	$8$	$-0.623744$	$21296/15$	$0.85611$	$3.24000$	$[0, 1, 0, 4, 0]$	\(y^2=x^3+x^2+4x\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.2, 20.12.0-4.c.1.2, $\ldots$	$[]$
120.b1	120a5	120.b	120a	$6$	$8$	\( 2^{3} \cdot 3 \cdot 5 \)	\( 2^{11} \cdot 3 \cdot 5^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.45	2B	$240$	$192$	$1$	$1$	$4$	$2$	$1$	$64$	$0.479999$	$1770025017602/75$	$1.12837$	$7.48338$	$[0, 1, 0, -3200, -70752]$	\(y^2=x^3+x^2-3200x-70752\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.f.1.3, 24.48.0-24.bj.1.7, $\ldots$	$[]$
120.b2	120a3	120.b	120a	$6$	$8$	\( 2^{3} \cdot 3 \cdot 5 \)	\( 2^{10} \cdot 3^{2} \cdot 5^{4} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.31	2Cs	$120$	$192$	$1$	$1$	$1$		$3$	$32$	$0.133425$	$868327204/5625$	$1.10029$	$5.74697$	$[0, 1, 0, -200, -1152]$	\(y^2=x^3+x^2-200x-1152\)	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.d.1.2, 24.96.0-24.k.1.1, 40.96.0-40.v.1.4, $\ldots$	$[]$
120.b3	120a6	120.b	120a	$6$	$8$	\( 2^{3} \cdot 3 \cdot 5 \)	\( - 2^{11} \cdot 3 \cdot 5^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.175	2B	$240$	$192$	$1$	$1$	$1$		$1$	$64$	$0.479999$	$-27995042/1171875$	$1.07729$	$6.07149$	$[0, 1, 0, -80, -2400]$	\(y^2=x^3+x^2-80x-2400\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.ba.1.1, 24.96.0-24.bo.1.2, 80.96.0.?, $\ldots$	$[]$
120.b4	120a2	120.b	120a	$6$	$8$	\( 2^{3} \cdot 3 \cdot 5 \)	\( 2^{8} \cdot 3^{4} \cdot 5^{2} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.26	2Cs	$120$	$192$	$1$	$1$	$1$		$7$	$16$	$-0.213148$	$3631696/2025$	$1.02576$	$4.31340$	$[0, 1, 0, -20, 0]$	\(y^2=x^3+x^2-20x\)	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.d.2.1, 20.48.0-20.c.1.1, 24.96.0-24.p.2.3, $\ldots$	$[]$
120.b5	120a1	120.b	120a	$6$	$8$	\( 2^{3} \cdot 3 \cdot 5 \)	\( 2^{4} \cdot 3^{2} \cdot 5 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.30	2B	$240$	$192$	$1$	$1$	$1$		$3$	$8$	$-0.559722$	$24918016/45$	$0.99237$	$4.13655$	$[0, 1, 0, -15, 18]$	\(y^2=x^3+x^2-15x+18\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 10.6.0.a.1, 16.48.0-16.f.2.3, $\ldots$	$[]$
120.b6	120a4	120.b	120a	$6$	$8$	\( 2^{3} \cdot 3 \cdot 5 \)	\( - 2^{10} \cdot 3^{8} \cdot 5 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.160	2B	$240$	$192$	$1$	$1$	$1$		$3$	$32$	$0.133425$	$54607676/32805$	$1.06524$	$5.16913$	$[0, 1, 0, 80, 80]$	\(y^2=x^3+x^2+80x+80\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.ba.2.2, 20.24.0-20.h.1.2, 40.96.0-40.bm.2.2, $\ldots$	$[]$