Elliptic curve search results

Results (21 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
3990.bb3	3990bb2	3990.bb	3990bb	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{2} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.24.0.5	2Cs	$15960$	$192$	$1$	$1$	$1$		$6$	$15360$	$1.187033$	$116844823575501841/3760263939600$	$0.95823$	$4.73972$	$[1, 0, 0, -10185, 383625]$	\(y^2+xy=x^3-10185x+383625\)	2.6.0.a.1, 4.24.0-4.b.1.3, 24.48.0-24.l.1.10, 152.48.0.?, 280.48.0.?, $\ldots$	$[]$
11970.c3	11970r2	11970.c	11970r	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{18} \cdot 5^{2} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.26	2Cs	$15960$	$192$	$1$	$1$	$1$		$2$	$122880$	$1.736340$	$116844823575501841/3760263939600$	$0.95823$	$4.88717$	$[1, -1, 0, -91665, -10357875]$	\(y^2+xy=x^3-x^2-91665x-10357875\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.4, 12.24.0-4.b.1.3, 24.48.0-24.l.1.7, $\ldots$	$[]$
19950.o3	19950g2	19950.o	19950g	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{8} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$15960$	$192$	$1$	$1$	$1$		$2$	$368640$	$1.991753$	$116844823575501841/3760263939600$	$0.95823$	$4.94458$	$[1, 1, 0, -254625, 47953125]$	\(y^2+xy=x^3+x^2-254625x+47953125\)	2.6.0.a.1, 4.12.0.b.1, 20.24.0-4.b.1.3, 24.24.0.l.1, 56.24.0-4.b.1.2, $\ldots$	$[]$
27930.ci3	27930cg2	27930.ci	27930cg	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{2} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$15960$	$192$	$1$	$1$	$1$		$2$	$737280$	$2.159988$	$116844823575501841/3760263939600$	$0.95823$	$4.97927$	$[1, 1, 1, -499066, -132082441]$	\(y^2+xy+y=x^3+x^2-499066x-132082441\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0.l.1, 28.24.0-4.b.1.3, 40.24.0-4.b.1.2, $\ldots$	$[]$
31920.ba3	31920bk2	31920.ba	31920bk	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{12} \cdot 5^{2} \cdot 7^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.24.0.6	2Cs	$15960$	$192$	$1$	$5.863560677$	$1$		$3$	$368640$	$1.880180$	$116844823575501841/3760263939600$	$0.95823$	$4.59140$	$[0, -1, 0, -162960, -24552000]$	\(y^2=x^3-x^2-162960x-24552000\)	2.6.0.a.1, 4.24.0-4.b.1.1, 24.48.0-24.l.1.3, 152.48.0.?, 280.48.0.?, $\ldots$	$[(5368/3, 256256/3)]$
59850.fe3	59850fh2	59850.fe	59850fh	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{4} \cdot 3^{18} \cdot 5^{8} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$15960$	$192$	$1$	$1$	$1$		$2$	$2949120$	$2.541058$	$116844823575501841/3760263939600$	$0.95823$	$5.05000$	$[1, -1, 1, -2291630, -1297026003]$	\(y^2+xy+y=x^3-x^2-2291630x-1297026003\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0.l.1, 40.24.0-4.b.1.4, 56.24.0-4.b.1.3, $\ldots$	$[]$
75810.x3	75810w2	75810.x	75810w	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{12} \cdot 5^{2} \cdot 7^{2} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.11	2Cs	$15960$	$192$	$1$	$8.275306991$	$1$		$2$	$5529600$	$2.659252$	$116844823575501841/3760263939600$	$0.95823$	$5.06998$	$[1, 1, 0, -3676792, -2638637456]$	\(y^2+xy=x^3+x^2-3676792x-2638637456\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.8, 24.48.0-24.l.1.20, 76.24.0.?, $\ldots$	$[(340828/11, 126917876/11)]$
83790.bi3	83790cn2	83790.bi	83790cn	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{18} \cdot 5^{2} \cdot 7^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$15960$	$192$	$1$	$3.128369506$	$1$		$8$	$5898240$	$2.709293$	$116844823575501841/3760263939600$	$0.95823$	$5.07819$	$[1, -1, 0, -4491594, 3561734308]$	\(y^2+xy=x^3-x^2-4491594x+3561734308\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0.l.1, 40.24.0-4.b.1.3, 56.24.0-4.b.1.4, $\ldots$	$[(1584, 19690)]$
95760.cu3	95760ea2	95760.cu	95760ea	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{18} \cdot 5^{2} \cdot 7^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.26	2Cs	$15960$	$192$	$1$	$3.953485272$	$1$		$7$	$2949120$	$2.429485$	$116844823575501841/3760263939600$	$0.95823$	$4.72633$	$[0, 0, 0, -1466643, 664370642]$	\(y^2=x^3-1466643x+664370642\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.4, 12.24.0-4.b.1.1, 24.48.0-24.l.1.12, $\ldots$	$[(286, 16380)]$
127680.d3	127680j2	127680.d	127680j	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{22} \cdot 3^{12} \cdot 5^{2} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.21	2Cs	$15960$	$192$	$1$	$1$	$1$		$3$	$2949120$	$2.226753$	$116844823575501841/3760263939600$	$0.95823$	$4.40376$	$[0, -1, 0, -651841, 197067841]$	\(y^2=x^3-x^2-651841x+197067841\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.2, 24.48.0-24.l.1.5, 152.48.0.?, $\ldots$	$[]$
127680.ew3	127680fi2	127680.ew	127680fi	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{22} \cdot 3^{12} \cdot 5^{2} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.20	2Cs	$15960$	$192$	$1$	$1$	$1$		$3$	$2949120$	$2.226753$	$116844823575501841/3760263939600$	$0.95823$	$4.40376$	$[0, 1, 0, -651841, -197067841]$	\(y^2=x^3+x^2-651841x-197067841\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.11, 24.48.0-24.l.1.11, 152.48.0.?, $\ldots$	$[]$
139650.ef3	139650ha2	139650.ef	139650ha	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{8} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.17	2Cs	$15960$	$192$	$1$	$1$	$1$		$2$	$17694720$	$2.964706$	$116844823575501841/3760263939600$	$0.95823$	$5.11794$	$[1, 0, 1, -12476651, -16485351802]$	\(y^2+xy+y=x^3-12476651x-16485351802\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 24.48.0-24.l.1.2, 76.24.0.?, $\ldots$	$[]$
159600.do3	159600bt2	159600.do	159600bt	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{12} \cdot 5^{8} \cdot 7^{2} \cdot 19^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$15960$	$192$	$1$	$2.727420158$	$1$		$33$	$8847360$	$2.684898$	$116844823575501841/3760263939600$	$0.95823$	$4.78063$	$[0, 1, 0, -4074008, -3077148012]$	\(y^2=x^3+x^2-4074008x-3077148012\)	2.6.0.a.1, 4.12.0.b.1, 20.24.0-4.b.1.1, 24.24.0.l.1, 56.24.0-4.b.1.7, $\ldots$	$[(-1268, 7182), (-1097, 8550)]$
223440.dt3	223440bv2	223440.dt	223440bv	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{12} \cdot 5^{2} \cdot 7^{8} \cdot 19^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$15960$	$192$	$1$	$2.085217768$	$1$		$37$	$17694720$	$2.853134$	$116844823575501841/3760263939600$	$0.95823$	$4.81394$	$[0, 1, 0, -7985056, 8437306100]$	\(y^2=x^3+x^2-7985056x+8437306100\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0.l.1, 28.24.0-4.b.1.1, 40.24.0-4.b.1.7, $\ldots$	$[(716, 55566), (1364, 9234)]$
227430.dg3	227430bq2	227430.dg	227430bq	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{18} \cdot 5^{2} \cdot 7^{2} \cdot 19^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.9	2Cs	$15960$	$192$	$1$	$1$	$1$		$2$	$44236800$	$3.208557$	$116844823575501841/3760263939600$	$0.95823$	$5.15282$	$[1, -1, 1, -33091133, 71210120181]$	\(y^2+xy+y=x^3-x^2-33091133x+71210120181\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.3, 24.48.0-24.l.1.13, 152.48.0.?, $\ldots$	$[]$
379050.kd3	379050kd2	379050.kd	379050kd	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{12} \cdot 5^{8} \cdot 7^{2} \cdot 19^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$15960$	$192$	$1$	$4.557401952$	$1$		$6$	$132710400$	$3.463970$	$116844823575501841/3760263939600$	$0.95823$	$5.18651$	$[1, 0, 0, -91919813, -329645842383]$	\(y^2+xy=x^3-91919813x-329645842383\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0.l.1, 28.24.0-4.b.1.2, 40.24.0-4.b.1.7, $\ldots$	$[(-4808, 36529)]$
383040.ki3	383040ki2	383040.ki	383040ki	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{22} \cdot 3^{18} \cdot 5^{2} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.24	2Cs	$15960$	$192$	$1$	$1$	$4$	$2$	$3$	$23592960$	$2.776058$	$116844823575501841/3760263939600$	$0.95823$	$4.54017$	$[0, 0, 0, -5866572, -5314965136]$	\(y^2=x^3-5866572x-5314965136\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.5, 24.48.0-24.l.1.9, 152.48.0.?, $\ldots$	$[]$
383040.lp3	383040lp2	383040.lp	383040lp	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{22} \cdot 3^{18} \cdot 5^{2} \cdot 7^{2} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.24	2Cs	$15960$	$192$	$1$	$4.108300908$	$1$		$7$	$23592960$	$2.776058$	$116844823575501841/3760263939600$	$0.95823$	$4.54017$	$[0, 0, 0, -5866572, 5314965136]$	\(y^2=x^3-5866572x+5314965136\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.5, 24.48.0-24.l.1.1, 152.48.0.?, $\ldots$	$[(860, 30096)]$
418950.ko3	418950ko2	418950.ko	418950ko	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{18} \cdot 5^{8} \cdot 7^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.9	2Cs	$15960$	$192$	$1$	$5.287545234$	$1$		$6$	$141557760$	$3.514011$	$116844823575501841/3760263939600$	$0.95823$	$5.19280$	$[1, -1, 1, -112289855, 445104498647]$	\(y^2+xy+y=x^3-x^2-112289855x+445104498647\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.3, 24.48.0-24.l.1.8, 152.48.0.?, $\ldots$	$[(4573, 162696)]$
478800.gk3	478800gk2	478800.gk	478800gk	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{18} \cdot 5^{8} \cdot 7^{2} \cdot 19^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$15960$	$192$	$1$	$1$	$1$		$3$	$70778880$	$3.234207$	$116844823575501841/3760263939600$	$0.95823$	$4.88306$	$[0, 0, 0, -36666075, 83046330250]$	\(y^2=x^3-36666075x+83046330250\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0.l.1, 40.24.0-4.b.1.4, 56.24.0-4.b.1.8, $\ldots$	$[]$
482790.dr3	482790dr2	482790.dr	482790dr	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( 2^{4} \cdot 3^{12} \cdot 5^{2} \cdot 7^{2} \cdot 11^{6} \cdot 19^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.3	2Cs	$175560$	$192$	$1$	$2.344068162$	$1$		$30$	$19660800$	$2.385983$	$116844823575501841/3760263939600$	$0.95823$	$4.10221$	$[1, 0, 1, -1232388, -511837262]$	\(y^2+xy+y=x^3-1232388x-511837262\)	2.6.0.a.1, 4.12.0.b.1, 24.24.0.l.1, 44.24.0-4.b.1.3, 152.24.0.?, $\ldots$	$[(-646, 4170), (-691, 3495)]$