Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (6 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
210.e6	210e2	210.e	210e	$8$	$16$	\( 2 \cdot 3 \cdot 5 \cdot 7 \)	\( 2^{8} \cdot 3^{8} \cdot 5^{4} \cdot 7^{2} \)	$0$	$\Z/2\Z\oplus\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.40	2Cs	$1$	$1$		$14$	$256$	$0.754708$	$135487869158881/51438240000$	$[1, 0, 0, -1070, 7812]$	\(y^2+xy=x^3-1070x+7812\)
46410.ck6	46410cn2	46410.ck	46410cn	$8$	$16$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17 \)	\( 2^{8} \cdot 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 13^{4} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.40	2Cs	$1$	$1$		$14$	$3145728$	$2.779636$	$72727020009972527154752161/265361167808100000000$	$[1, 0, 0, -8696090, 9838496100]$	\(y^2+xy=x^3-8696090x+9838496100\)
82110.bs5	82110bt2	82110.bs	82110bt	$8$	$16$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 23 \)	\( 2^{16} \cdot 3^{8} \cdot 5^{8} \cdot 7^{2} \cdot 17^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.40	2Cs	$2.034865242$	$1$		$36$	$14680064$	$3.300953$	$13350979617415439280823624321/363628103290905600000000$	$[1, 0, 0, -49423080, 130545230400]$	\(y^2+xy=x^3-49423080x+130545230400\)
110670.cm5	110670cp2	110670.cm	110670cp	$8$	$16$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 31 \)	\( 2^{16} \cdot 3^{8} \cdot 5^{8} \cdot 7^{8} \cdot 17^{2} \cdot 31^{2} \)	$0$	$\Z/2\Z\oplus\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.40	2Cs	$1$	$1$		$14$	$98566144$	$4.068329$	$1305195379419707692723460338574401/268915325631261926400000000$	$[1, 0, 0, -2276760100, 41806588162832]$	\(y^2+xy=x^3-2276760100x+41806588162832\)
249690.cj6	249690cj2	249690.cj	249690cj	$8$	$16$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 29 \cdot 41 \)	\( 2^{8} \cdot 3^{8} \cdot 5^{8} \cdot 7^{8} \cdot 29^{4} \cdot 41^{2} \)	$1$	$\Z/2\Z\oplus\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.40	2Cs	$4.745614618$	$1$		$22$	$190840832$	$4.033775$	$33716734605576776462761920782881/4496908623986020832100000000$	$[1, 0, 0, -673039570, -5895575919100]$	\(y^2+xy=x^3-673039570x-5895575919100\)
266910.ck5	266910ck2	266910.ck	266910ck	$8$	$16$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 31 \cdot 41 \)	\( 2^{16} \cdot 3^{16} \cdot 5^{8} \cdot 7^{4} \cdot 31^{2} \cdot 41^{4} \)	$1$	$\Z/2\Z\oplus\Z/8\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.96.0.40	2Cs	$5.628328977$	$1$		$22$	$1660944384$	$5.027771$	$279321867933339260687315798724918183361/7185070196198556975129600000000$	$[1, 0, 0, -136184310140, 19343222133507600]$	\(y^2+xy=x^3-136184310140x+19343222133507600\)