Elliptic curve search results

Results (24 matches)

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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
5070.i1	5070j1	5070.i	5070j	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{5} \cdot 3^{4} \cdot 5 \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$87360$	$1.900578$	$-79370312059129/12960$	$1.18524$	$6.15686$	$[1, 0, 1, -836554, -294572068]$	\(y^2+xy+y=x^3-836554x-294572068\)	40.2.0.a.1	$[ ]$
5070.x1	5070x1	5070.x	5070x	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{5} \cdot 3^{4} \cdot 5 \cdot 13^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$6720$	$0.618102$	$-79370312059129/12960$	$1.18524$	$4.35290$	$[1, 0, 0, -4950, -134460]$	\(y^2+xy=x^3-4950x-134460\)	40.2.0.a.1	$[ ]$
15210.l1	15210p1	15210.l	15210p	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \)	\( - 2^{5} \cdot 3^{10} \cdot 5 \cdot 13^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$53760$	$1.167408$	$-79370312059129/12960$	$1.18524$	$4.54081$	$[1, -1, 0, -44550, 3630420]$	\(y^2+xy=x^3-x^2-44550x+3630420\)	40.2.0.a.1	$[ ]$
15210.bk1	15210bt1	15210.bk	15210bt	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \)	\( - 2^{5} \cdot 3^{10} \cdot 5 \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$698880$	$2.449883$	$-79370312059129/12960$	$1.18524$	$6.13896$	$[1, -1, 1, -7528982, 7953445829]$	\(y^2+xy+y=x^3-x^2-7528982x+7953445829\)	40.2.0.a.1	$[ ]$
25350.b1	25350j1	25350.b	25350j	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 2^{5} \cdot 3^{4} \cdot 5^{7} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$5.738402462$	$1$		$2$	$161280$	$1.422821$	$-79370312059129/12960$	$1.18524$	$4.61432$	$[1, 1, 0, -123750, -16807500]$	\(y^2+xy=x^3+x^2-123750x-16807500\)	40.2.0.a.1	$[(4455, 294210)]$
25350.cp1	25350cb1	25350.cp	25350cb	$1$	$1$	\( 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 2^{5} \cdot 3^{4} \cdot 5^{7} \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$2096640$	$2.705296$	$-79370312059129/12960$	$1.18524$	$6.13196$	$[1, 1, 1, -20913838, -36821508469]$	\(y^2+xy+y=x^3+x^2-20913838x-36821508469\)	40.2.0.a.1	$[ ]$
40560.o1	40560bl1	40560.o	40560bl	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{17} \cdot 3^{4} \cdot 5 \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$2096640$	$2.593723$	$-79370312059129/12960$	$1.18524$	$5.73416$	$[0, -1, 0, -13384856, 18852612336]$	\(y^2=x^3-x^2-13384856x+18852612336\)	40.2.0.a.1	$[ ]$
40560.p1	40560bx1	40560.p	40560bx	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{17} \cdot 3^{4} \cdot 5 \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$0.689110649$	$1$		$6$	$161280$	$1.311249$	$-79370312059129/12960$	$1.18524$	$4.28374$	$[0, -1, 0, -79200, 8605440]$	\(y^2=x^3-x^2-79200x+8605440\)	40.2.0.a.1	$[(162, 18)]$
76050.dc1	76050bw1	76050.dc	76050bw	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} \)	\( - 2^{5} \cdot 3^{10} \cdot 5^{7} \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$16773120$	$3.254601$	$-79370312059129/12960$	$1.18524$	$6.11906$	$[1, -1, 0, -188224542, 993992504116]$	\(y^2+xy=x^3-x^2-188224542x+993992504116\)	40.2.0.a.1	$[ ]$
76050.de1	76050fe1	76050.de	76050fe	$1$	$1$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} \)	\( - 2^{5} \cdot 3^{10} \cdot 5^{7} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$0.311060534$	$1$		$8$	$1290240$	$1.972128$	$-79370312059129/12960$	$1.18524$	$4.74977$	$[1, -1, 1, -1113755, 452688747]$	\(y^2+xy+y=x^3-x^2-1113755x+452688747\)	40.2.0.a.1	$[(599, 150)]$
121680.b1	121680ee1	121680.b	121680ee	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 13^{2} \)	\( - 2^{17} \cdot 3^{10} \cdot 5 \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$7.840797090$	$1$		$0$	$1290240$	$1.860556$	$-79370312059129/12960$	$1.18524$	$4.44477$	$[0, 0, 0, -712803, -231634078]$	\(y^2=x^3-712803x-231634078\)	40.2.0.a.1	$[(48673/7, 2181024/7)]$
121680.fs1	121680fk1	121680.fs	121680fk	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 13^{2} \)	\( - 2^{17} \cdot 3^{10} \cdot 5 \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$49$	$7$	$0$	$16773120$	$3.143028$	$-79370312059129/12960$	$1.18524$	$5.75910$	$[0, 0, 0, -120463707, -508900069366]$	\(y^2=x^3-120463707x-508900069366\)	40.2.0.a.1	$[ ]$
162240.bz1	162240ij1	162240.bz	162240ij	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{23} \cdot 3^{4} \cdot 5 \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$13.00072661$	$1$		$0$	$1290240$	$1.657824$	$-79370312059129/12960$	$1.18524$	$4.13540$	$[0, -1, 0, -316801, -68526719]$	\(y^2=x^3-x^2-316801x-68526719\)	40.2.0.a.1	$[(2056171/43, 2454620940/43)]$
162240.cc1	162240gs1	162240.cc	162240gs	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{23} \cdot 3^{4} \cdot 5 \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$16773120$	$2.940296$	$-79370312059129/12960$	$1.18524$	$5.41821$	$[0, -1, 0, -53539425, -150767359263]$	\(y^2=x^3-x^2-53539425x-150767359263\)	40.2.0.a.1	$[ ]$
162240.eg1	162240y1	162240.eg	162240y	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{23} \cdot 3^{4} \cdot 5 \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$0.530946305$	$1$		$4$	$1290240$	$1.657824$	$-79370312059129/12960$	$1.18524$	$4.13540$	$[0, 1, 0, -316801, 68526719]$	\(y^2=x^3+x^2-316801x+68526719\)	40.2.0.a.1	$[(287, 1152)]$
162240.ii1	162240w1	162240.ii	162240w	$1$	$1$	\( 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} \)	\( - 2^{23} \cdot 3^{4} \cdot 5 \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$16773120$	$2.940296$	$-79370312059129/12960$	$1.18524$	$5.41821$	$[0, 1, 0, -53539425, 150767359263]$	\(y^2=x^3+x^2-53539425x+150767359263\)	40.2.0.a.1	$[ ]$
202800.fs1	202800bn1	202800.fs	202800bn	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 2^{17} \cdot 3^{4} \cdot 5^{7} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$0.749979065$	$1$		$4$	$50319360$	$3.398441$	$-79370312059129/12960$	$1.18524$	$5.76917$	$[0, 1, 0, -334621408, 2355907299188]$	\(y^2=x^3+x^2-334621408x+2355907299188\)	40.2.0.a.1	$[(10703, 25350)]$
202800.kl1	202800db1	202800.kl	202800db	$1$	$1$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( - 2^{17} \cdot 3^{4} \cdot 5^{7} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$0.808601344$	$1$		$4$	$3870720$	$2.115967$	$-79370312059129/12960$	$1.18524$	$4.50978$	$[0, 1, 0, -1980008, 1071719988]$	\(y^2=x^3+x^2-1980008x+1071719988\)	40.2.0.a.1	$[(814, 96)]$
248430.bw1	248430bw1	248430.bw	248430bw	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{5} \cdot 3^{4} \cdot 5 \cdot 7^{6} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$3.913237855$	$1$		$0$	$20442240$	$2.873531$	$-79370312059129/12960$	$1.18524$	$5.16788$	$[1, 1, 0, -40991122, 100997228116]$	\(y^2+xy=x^3+x^2-40991122x+100997228116\)	40.2.0.a.1	$[(12955/2, 364253/2)]$
248430.go1	248430go1	248430.go	248430go	$1$	$1$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} \)	\( - 2^{5} \cdot 3^{4} \cdot 5 \cdot 7^{6} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1.375746247$	$1$		$2$	$1572480$	$1.591057$	$-79370312059129/12960$	$1.18524$	$3.92907$	$[1, 1, 1, -242551, 45877229]$	\(y^2+xy+y=x^3+x^2-242551x+45877229\)	40.2.0.a.1	$[(287, -54)]$
486720.a1	486720a1	486720.a	486720a	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} \)	\( - 2^{23} \cdot 3^{10} \cdot 5 \cdot 13^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$1$		$0$	$134184960$	$3.489605$	$-79370312059129/12960$	$1.18524$	$5.46702$	$[0, 0, 0, -481854828, 4071200554928]$	\(y^2=x^3-481854828x+4071200554928\)	40.2.0.a.1	$[ ]$
486720.il1	486720il1	486720.il	486720il	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} \)	\( - 2^{23} \cdot 3^{10} \cdot 5 \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$31.15048406$	$1$		$0$	$134184960$	$3.489605$	$-79370312059129/12960$	$1.18524$	$5.46702$	$[0, 0, 0, -481854828, -4071200554928]$	\(y^2=x^3-481854828x-4071200554928\)	40.2.0.a.1	$[(13155211421293578/715261, 269062408394258635661440/715261)]$
486720.im1	486720im1	486720.im	486720im	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} \)	\( - 2^{23} \cdot 3^{10} \cdot 5 \cdot 13^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$1$	$9$	$3$	$0$	$10321920$	$2.207130$	$-79370312059129/12960$	$1.18524$	$4.29183$	$[0, 0, 0, -2851212, -1853072624]$	\(y^2=x^3-2851212x-1853072624\)	40.2.0.a.1	$[ ]$
486720.qx1	486720qx1	486720.qx	486720qx	$1$	$1$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} \)	\( - 2^{23} \cdot 3^{10} \cdot 5 \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$40$	$2$	$0$	$4.399784083$	$1$		$0$	$10321920$	$2.207130$	$-79370312059129/12960$	$1.18524$	$4.29183$	$[0, 0, 0, -2851212, 1853072624]$	\(y^2=x^3-2851212x+1853072624\)	40.2.0.a.1	$[(47230/7, 203904/7)]$

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