LMFDB - Elliptic curve search results

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio	Manin constant

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Results (28 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	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
5408.a1	5408g1	5408.a	5408g	$1$	$1$	$ 2^{5} \cdot 13^{2} $	$ - 2^{9} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$22464$	$1.250874$	$-74088$	$0.92990$	$4.71855$	$[0, 0, 0, -15379, -742586]$	$y^2=x^3-15379x-742586$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
5408.b1	5408m1	5408.b	5408m	$1$	$1$	$ 2^{5} \cdot 13^{2} $	$ - 2^{9} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$0.943302495$	$1$		$4$	$1728$	$-0.031601$	$-74088$	$0.92990$	$2.92814$	$[0, 0, 0, -91, -338]$	$y^2=x^3-91x-338$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(13, 26)]$
5408.l1	5408l1	5408.l	5408l	$1$	$1$	$ 2^{5} \cdot 13^{2} $	$ - 2^{9} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$3.547654043$	$1$		$0$	$22464$	$1.250874$	$-74088$	$0.92990$	$4.71855$	$[0, 0, 0, -15379, 742586]$	$y^2=x^3-15379x+742586$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(1690/3, 57122/3)]$
5408.m1	5408f1	5408.m	5408f	$1$	$1$	$ 2^{5} \cdot 13^{2} $	$ - 2^{9} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$1728$	$-0.031601$	$-74088$	$0.92990$	$2.92814$	$[0, 0, 0, -91, 338]$	$y^2=x^3-91x+338$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
10816.a1	10816x1	10816.a	10816x	$1$	$1$	$ 2^{6} \cdot 13^{2} $	$ - 2^{15} \cdot 13^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$0.213660420$	$1$		$22$	$6912$	$0.314972$	$-74088$	$0.92990$	$3.15737$	$[0, 0, 0, -364, 2704]$	$y^2=x^3-364x+2704$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(26, 104), (10, 8)]$
10816.e1	10816w1	10816.e	10816w	$1$	$1$	$ 2^{6} \cdot 13^{2} $	$ - 2^{15} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$89856$	$1.597446$	$-74088$	$0.92990$	$4.81417$	$[0, 0, 0, -61516, 5940688]$	$y^2=x^3-61516x+5940688$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
10816.bk1	10816v1	10816.bk	10816v	$1$	$1$	$ 2^{6} \cdot 13^{2} $	$ - 2^{15} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$6912$	$0.314972$	$-74088$	$0.92990$	$3.15737$	$[0, 0, 0, -364, -2704]$	$y^2=x^3-364x-2704$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
10816.bo1	10816u1	10816.bo	10816u	$1$	$1$	$ 2^{6} \cdot 13^{2} $	$ - 2^{15} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$9$	$3$	$0$	$89856$	$1.597446$	$-74088$	$0.92990$	$4.81417$	$[0, 0, 0, -61516, -5940688]$	$y^2=x^3-61516x-5940688$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
48672.f1	48672cb1	48672.f	48672cb	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 3^{6} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$24192$	$0.517705$	$-74088$	$0.92990$	$2.94277$	$[0, 0, 0, -819, -9126]$	$y^2=x^3-819x-9126$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
48672.g1	48672z1	48672.g	48672z	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 3^{6} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$0.719988888$	$1$		$4$	$24192$	$0.517705$	$-74088$	$0.92990$	$2.94277$	$[0, 0, 0, -819, 9126]$	$y^2=x^3-819x+9126$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(13, 26)]$
48672.bw1	48672ca1	48672.bw	48672ca	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 3^{6} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$314496$	$1.800179$	$-74088$	$0.92990$	$4.36869$	$[0, 0, 0, -138411, 20049822]$	$y^2=x^3-138411x+20049822$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
48672.bx1	48672y1	48672.bx	48672y	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 3^{6} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$34.14031577$	$1$		$0$	$314496$	$1.800179$	$-74088$	$0.92990$	$4.36869$	$[0, 0, 0, -138411, -20049822]$	$y^2=x^3-138411x-20049822$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(28620893777071102/3636761, 4765040348837498252768492/3636761)]$
97344.p1	97344dm1	97344.p	97344dm	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 3^{6} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1.439155616$	$1$		$4$	$1257984$	$2.146751$	$-74088$	$0.92990$	$4.46713$	$[0, 0, 0, -553644, 160398576]$	$y^2=x^3-553644x+160398576$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(-338, 17576)]$
97344.s1	97344dl1	97344.s	97344dl	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 3^{6} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$6.340147716$	$1$		$2$	$1257984$	$2.146751$	$-74088$	$0.92990$	$4.46713$	$[0, 0, 0, -553644, -160398576]$	$y^2=x^3-553644x-160398576$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(2266, 101096)]$
97344.fw1	97344dj1	97344.fw	97344dj	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 3^{6} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$6.919758403$	$1$		$0$	$96768$	$0.864278$	$-74088$	$0.92990$	$3.12727$	$[0, 0, 0, -3276, -73008]$	$y^2=x^3-3276x-73008$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(2821/5, 124631/5)]$
97344.gb1	97344di1	97344.gb	97344di	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 3^{6} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1.841181522$	$1$		$2$	$96768$	$0.864278$	$-74088$	$0.92990$	$3.12727$	$[0, 0, 0, -3276, 73008]$	$y^2=x^3-3276x+73008$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(52, 208)]$
135200.a1	135200bx1	135200.a	135200bx	$1$	$1$	$ 2^{5} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 5^{6} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$2426112$	$2.055592$	$-74088$	$0.92990$	$4.25033$	$[0, 0, 0, -384475, 92823250]$	$y^2=x^3-384475x+92823250$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
135200.b1	135200a1	135200.b	135200a	$1$	$1$	$ 2^{5} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 5^{6} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1.739392328$	$1$		$2$	$186624$	$0.773117$	$-74088$	$0.92990$	$2.94772$	$[0, 0, 0, -2275, 42250]$	$y^2=x^3-2275x+42250$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(26, 26)]$
135200.dl1	135200dm1	135200.dl	135200dm	$1$	$1$	$ 2^{5} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 5^{6} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$186624$	$0.773117$	$-74088$	$0.92990$	$2.94772$	$[0, 0, 0, -2275, -42250]$	$y^2=x^3-2275x-42250$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
135200.dm1	135200bv1	135200.dm	135200bv	$1$	$1$	$ 2^{5} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 5^{6} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$40.51143270$	$1$		$0$	$2426112$	$2.055592$	$-74088$	$0.92990$	$4.25033$	$[0, 0, 0, -384475, -92823250]$	$y^2=x^3-384475x-92823250$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(36676202300014108429/18507225, 222110577515208408953755467158/18507225)]$
264992.a1	264992a1	264992.a	264992a	$1$	$1$	$ 2^{5} \cdot 7^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 7^{6} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$3.476720012$	$1$		$2$	$653184$	$0.941354$	$-74088$	$0.92990$	$2.95054$	$[0, 0, 0, -4459, -115934]$	$y^2=x^3-4459x-115934$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(78, 104)]$
264992.h1	264992h1	264992.h	264992h	$1$	$1$	$ 2^{5} \cdot 7^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 7^{6} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$8491392$	$2.223827$	$-74088$	$0.92990$	$4.18295$	$[0, 0, 0, -753571, -254706998]$	$y^2=x^3-753571x-254706998$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
264992.dr1	264992dr1	264992.dr	264992dr	$1$	$1$	$ 2^{5} \cdot 7^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 7^{6} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$653184$	$0.941354$	$-74088$	$0.92990$	$2.95054$	$[0, 0, 0, -4459, 115934]$	$y^2=x^3-4459x+115934$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
264992.dy1	264992dy1	264992.dy	264992dy	$1$	$1$	$ 2^{5} \cdot 7^{2} \cdot 13^{2} $	$ - 2^{9} \cdot 7^{6} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$17.99580116$	$1$		$0$	$8491392$	$2.223827$	$-74088$	$0.92990$	$4.18295$	$[0, 0, 0, -753571, 254706998]$	$y^2=x^3-753571x+254706998$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[(8127982837/4089, 123386621298382/4089)]$
270400.g1	270400g1	270400.g	270400g	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 5^{6} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$746496$	$1.119692$	$-74088$	$0.92990$	$3.11687$	$[0, 0, 0, -9100, -338000]$	$y^2=x^3-9100x-338000$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
270400.l1	270400l1	270400.l	270400l	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 5^{6} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$9704448$	$2.402164$	$-74088$	$0.92990$	$4.34729$	$[0, 0, 0, -1537900, -742586000]$	$y^2=x^3-1537900x-742586000$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
270400.kb1	270400kb1	270400.kb	270400kb	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 5^{6} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$4$	$2$	$0$	$9704448$	$2.402164$	$-74088$	$0.92990$	$4.34729$	$[0, 0, 0, -1537900, 742586000]$	$y^2=x^3-1537900x+742586000$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$
270400.kg1	270400kg1	270400.kg	270400kg	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 5^{6} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$3$	3.3.0.1	3Nn	$312$	$12$	$1$	$1$	$1$		$0$	$746496$	$1.119692$	$-74088$	$0.92990$	$3.11687$	$[0, 0, 0, -9100, 338000]$	$y^2=x^3-9100x+338000$	3.3.0.a.1, 24.6.0.m.1, 104.2.0.?, 156.6.0.?, 312.12.1.?	$[ ]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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