Elliptic curve search results

Results (4 matches)

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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
300.1-a2	300.1-a	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 5^{16} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B	$1$	\( 2 \cdot 3 \)	$0.114155808$	$3.601411123$	0.900723170	\( -\frac{40960}{27} \)	\( \bigl[0\) , \( -1\) , \( a\) , \( -83\) , \( -393\bigr] \)	${y}^2+a{y}={x}^3-{x}^2-83{x}-393$
300.1-d2	300.1-d	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{16} \cdot 3^{6} \cdot 5^{4} \)	$4.07389$	$(2,a), (3,a), (5,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B	$1$	\( 2 \cdot 3 \)	$0.758867116$	$3.601411123$	5.987686514	\( -\frac{40960}{27} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( -23\bigr] \)	${y}^2={x}^3-{x}^2-13{x}-23$
300.1-e2	300.1-e	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 5^{4} \)	$4.07389$	$(2,a), (3,a), (5,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.2	$1$	\( 2 \cdot 3 \)	$1$	$3.601411123$	3.945148222	\( -\frac{40960}{27} \)	\( \bigl[0\) , \( 1\) , \( a\) , \( -3\) , \( 3\bigr] \)	${y}^2+a{y}={x}^3+{x}^2-3{x}+3$
300.1-h2	300.1-h	$2$	$3$	\(\Q(\sqrt{-30}) \)	$2$	$[0, 1]$	300.1	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( 2^{4} \cdot 3^{18} \cdot 5^{4} \)	$4.07389$	$(2,a), (3,a), (5,a)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3B.1.1	$1$	\( 2 \cdot 3^{3} \)	$1$	$3.601411123$	3.945148222	\( -\frac{40960}{27} \)	\( \bigl[0\) , \( 0\) , \( a\) , \( -30\) , \( 100\bigr] \)	${y}^2+a{y}={x}^3-30{x}+100$

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  *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.