Elliptic curve search results

Results (20 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
14450.b1	14450p2	14450.b	14450p	$2$	$17$	\( 2 \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{17} \cdot 5^{3} \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$11.35371364$	$1$		$0$	$208080$	$2.002991$	$-882216989/131072$	$0.95690$	$5.04471$	$1$	$[1, 0, 1, -190891, -36002922]$	\(y^2+xy+y=x^3-190891x-36002922\)	17.72.1.b.2, 40.2.0.a.1, 85.288.5.?, 136.144.5.?, 680.576.17.?	$[(147018/13, 45982377/13)]$	$1$
14450.o2	14450n1	14450.o	14450n	$2$	$17$	\( 2 \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{17} \cdot 5^{3} \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$1$	$1$		$0$	$12240$	$0.586384$	$-882216989/131072$	$0.95690$	$3.26997$	$1$	$[1, 1, 0, -660, -7600]$	\(y^2+xy=x^3+x^2-660x-7600\)	17.72.1.b.2, 40.2.0.a.1, 85.288.5.?, 136.144.5.?, 680.576.17.?	$[ ]$	$1$
14450.w2	14450bk1	14450.w	14450bk	$2$	$17$	\( 2 \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{17} \cdot 5^{9} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$0.767553453$	$1$		$4$	$61200$	$1.391104$	$-882216989/131072$	$0.95690$	$4.27813$	$1$	$[1, 0, 0, -16513, -916983]$	\(y^2+xy=x^3-16513x-916983\)	17.72.1.b.2, 40.2.0.a.1, 85.288.5.?, 136.144.5.?, 680.576.17.?	$[(202, 1899)]$	$1$
14450.bh1	14450bl2	14450.bh	14450bl	$2$	$17$	\( 2 \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{17} \cdot 5^{9} \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$1$	$1$		$0$	$1040400$	$2.807709$	$-882216989/131072$	$0.95690$	$6.05287$	$1$	$[1, 1, 1, -4772263, -4500365219]$	\(y^2+xy+y=x^3+x^2-4772263x-4500365219\)	17.72.1.b.2, 40.2.0.a.1, 85.288.5.?, 136.144.5.?, 680.576.17.?	$[ ]$	$1$
115600.r1	115600dh2	115600.r	115600dh	$2$	$17$	\( 2^{4} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{29} \cdot 5^{9} \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$1$	$1$		$0$	$24969600$	$3.500858$	$-882216989/131072$	$0.95690$	$5.68670$	$1$	$[0, 1, 0, -76356208, 287870661588]$	\(y^2=x^3+x^2-76356208x+287870661588\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 340.288.5.?, $\ldots$	$[ ]$	$1$
115600.s2	115600dc1	115600.s	115600dc	$2$	$17$	\( 2^{4} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{29} \cdot 5^{3} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$1.069787957$	$1$		$4$	$293760$	$1.279531$	$-882216989/131072$	$0.95690$	$3.40018$	$1$	$[0, 1, 0, -10568, 465268]$	\(y^2=x^3+x^2-10568x+465268\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 340.288.5.?, $\ldots$	$[(478, 10240)]$	$1$
115600.co1	115600dg2	115600.co	115600dg	$2$	$17$	\( 2^{4} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{29} \cdot 5^{3} \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$1$	$1$		$0$	$4993920$	$2.696136$	$-882216989/131072$	$0.95690$	$4.85836$	$1$	$[0, -1, 0, -3054248, 2304186992]$	\(y^2=x^3-x^2-3054248x+2304186992\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 340.288.5.?, $\ldots$	$[ ]$	$1$
115600.cp2	115600db1	115600.cp	115600db	$2$	$17$	\( 2^{4} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{29} \cdot 5^{9} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$8.988131386$	$1$		$0$	$1468800$	$2.084251$	$-882216989/131072$	$0.95690$	$4.22852$	$1$	$[0, -1, 0, -264208, 58686912]$	\(y^2=x^3-x^2-264208x+58686912\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 340.288.5.?, $\ldots$	$[(150922/21, 26571250/21)]$	$1$
130050.o1	130050dq2	130050.o	130050dq	$2$	$17$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{17} \cdot 3^{6} \cdot 5^{9} \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$2040$	$576$	$17$	$1$	$4$	$2$	$0$	$24969600$	$3.357018$	$-882216989/131072$	$0.95690$	$5.48323$	$1$	$[1, -1, 0, -42950367, 121466910541]$	\(y^2+xy=x^3-x^2-42950367x+121466910541\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 255.288.5.?, $\ldots$	$[ ]$	$1$
130050.dh2	130050eg1	130050.dh	130050eg	$2$	$17$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{17} \cdot 3^{6} \cdot 5^{9} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$2040$	$576$	$17$	$4.848739324$	$1$		$2$	$1468800$	$1.940409$	$-882216989/131072$	$0.95690$	$4.03964$	$1$	$[1, -1, 0, -148617, 24758541]$	\(y^2+xy=x^3-x^2-148617x+24758541\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 255.288.5.?, $\ldots$	$[(45, 4239)]$	$1$
130050.em2	130050e1	130050.em	130050e	$2$	$17$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{17} \cdot 3^{6} \cdot 5^{3} \cdot 17^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$2040$	$576$	$17$	$0.331973079$	$1$		$20$	$293760$	$1.135691$	$-882216989/131072$	$0.95690$	$3.21959$	$1$	$[1, -1, 1, -5945, 199257]$	\(y^2+xy+y=x^3-x^2-5945x+199257\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 255.288.5.?, $\ldots$	$[(39, 140), (-25, 588)]$	$1$
130050.gu1	130050v2	130050.gu	130050v	$2$	$17$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{17} \cdot 3^{6} \cdot 5^{3} \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$2040$	$576$	$17$	$0.318134612$	$1$		$8$	$4993920$	$2.552296$	$-882216989/131072$	$0.95690$	$4.66319$	$1$	$[1, -1, 1, -1718015, 972078887]$	\(y^2+xy+y=x^3-x^2-1718015x+972078887\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 255.288.5.?, $\ldots$	$[(795, 10006)]$	$1$
462400.v2	462400v1	462400.v	462400v	$2$	$17$	\( 2^{6} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{35} \cdot 5^{9} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$1.676962834$	$1$		$4$	$11750400$	$2.430824$	$-882216989/131072$	$0.95690$	$4.09795$	$1$	$[0, 1, 0, -1056833, 468438463]$	\(y^2=x^3+x^2-1056833x+468438463\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 170.288.5.?, $\ldots$	$[(687, 8192)]$	$1$
462400.w1	462400w2	462400.w	462400w	$2$	$17$	\( 2^{6} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{35} \cdot 5^{9} \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$18.81655676$	$1$		$0$	$199756800$	$3.847431$	$-882216989/131072$	$0.95690$	$5.40116$	$1$	$[0, 1, 0, -305424833, -2303270717537]$	\(y^2=x^3+x^2-305424833x-2303270717537\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 340.288.5.?, $\ldots$	$[(102107494173/2041, 18892962815628500/2041)]$	$1$
462400.x1	462400x2	462400.x	462400x	$2$	$17$	\( 2^{6} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{35} \cdot 5^{3} \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$1$	$1$		$0$	$39951360$	$3.042713$	$-882216989/131072$	$0.95690$	$4.66086$	$1$	$[0, 1, 0, -12216993, 18421278943]$	\(y^2=x^3+x^2-12216993x+18421278943\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 170.288.5.?, $\ldots$	$[ ]$	$1$
462400.y2	462400y1	462400.y	462400y	$2$	$17$	\( 2^{6} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{35} \cdot 5^{3} \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$1$	$1$		$0$	$2350080$	$1.626104$	$-882216989/131072$	$0.95690$	$3.35765$	$1$	$[0, 1, 0, -42273, -3764417]$	\(y^2=x^3+x^2-42273x-3764417\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 340.288.5.?, $\ldots$	$[ ]$	$1$
462400.io2	462400io1	462400.io	462400io	$2$	$17$	\( 2^{6} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{35} \cdot 5^{3} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$7.028686712$	$1$		$0$	$2350080$	$1.626104$	$-882216989/131072$	$0.95690$	$3.35765$	$1$	$[0, -1, 0, -42273, 3764417]$	\(y^2=x^3-x^2-42273x+3764417\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 170.288.5.?, $\ldots$	$[(-872/3, 71135/3)]$	$1$
462400.ip1	462400ip2	462400.ip	462400ip	$2$	$17$	\( 2^{6} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{35} \cdot 5^{3} \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$49.79184117$	$1$		$0$	$39951360$	$3.042713$	$-882216989/131072$	$0.95690$	$4.66086$	$1$	$[0, -1, 0, -12216993, -18421278943]$	\(y^2=x^3-x^2-12216993x-18421278943\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 340.288.5.?, $\ldots$	$[(1334080774511245760260553/6932361673, 1527935520032823385156449512453283840/6932361673)]$	$1$
462400.iq1	462400iq2	462400.iq	462400iq	$2$	$17$	\( 2^{6} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{35} \cdot 5^{9} \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$1$	$4$	$2$	$0$	$199756800$	$3.847431$	$-882216989/131072$	$0.95690$	$5.40116$	$1$	$[0, -1, 0, -305424833, 2303270717537]$	\(y^2=x^3-x^2-305424833x+2303270717537\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 170.288.5.?, $\ldots$	$[ ]$	$1$
462400.ir2	462400ir1	462400.ir	462400ir	$2$	$17$	\( 2^{6} \cdot 5^{2} \cdot 17^{2} \)	\( - 2^{35} \cdot 5^{9} \cdot 17^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$17$	17.72.1.2	17B.4.2	$680$	$576$	$17$	$1$	$9$	$3$	$0$	$11750400$	$2.430824$	$-882216989/131072$	$0.95690$	$4.09795$	$1$	$[0, -1, 0, -1056833, -468438463]$	\(y^2=x^3-x^2-1056833x-468438463\)	17.72.1.b.2, 40.2.0.a.1, 85.144.5.?, 136.144.5.?, 340.288.5.?, $\ldots$	$[ ]$	$1$

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