Elliptic curve search results

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree/signature	Bad \(p\)	$\Q$-curves	Torsion structure	CM
Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image
j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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Results (3 matches)

 

Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
882.1-a1	882.1-a	$6$	$8$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	882.1	\( 2 \cdot 3^{2} \cdot 7^{2} \)	\( 2^{16} \cdot 3^{4} \cdot 7^{2} \)	$0.97395$	$(a+1), (3), (7)$	$0$	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{5} \)	$1$	$2.740367332$	1.370183666	\( -\frac{7189057}{16128} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4{x}+5$
7938.1-a1	7938.1-a	$6$	$8$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	7938.1	\( 2 \cdot 3^{4} \cdot 7^{2} \)	\( 2^{16} \cdot 3^{16} \cdot 7^{2} \)	$1.68693$	$(a+1), (3), (7)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$1$	$0.913455777$	1.826911554	\( -\frac{7189057}{16128} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( -176\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-36{x}-176$
43218.1-g1	43218.1-g	$6$	$8$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	43218.1	\( 2 \cdot 3^{2} \cdot 7^{4} \)	\( 2^{16} \cdot 3^{4} \cdot 7^{14} \)	$2.57682$	$(a+1), (3), (7)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{7} \)	$1.155405907$	$0.391481047$	7.237112237	\( -\frac{7189057}{16128} \)	\( \bigl[i\) , \( 0\) , \( 0\) , \( -197\) , \( 2367\bigr] \)	${y}^2+i{x}{y}={x}^{3}-197{x}+2367$

 

  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.