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
60.1-a6	60.1-a	$8$	$12$	\(\Q(\sqrt{-195}) \)	$2$	$[0, 1]$	60.1	\( 2^{2} \cdot 3 \cdot 5 \)	\( 2^{12} \cdot 3^{4} \cdot 5^{12} \cdot 7^{12} \)	$3.47291$	$(3,a+1), (5,a+2), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B	$4$	\( 2^{5} \cdot 3^{2} \)	$1$	$0.647145070$	6.673395029	\( \frac{4102915888729}{9000000} \)	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -332 a + 16389\) , \( -112322 a - 181450\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^3-a{x}^2+\left(-332a+16389\right){x}-112322a-181450$
60.1-b6	60.1-b	$8$	$12$	\(\Q(\sqrt{-195}) \)	$2$	$[0, 1]$	60.1	\( 2^{2} \cdot 3 \cdot 5 \)	\( 2^{12} \cdot 3^{4} \cdot 5^{24} \)	$3.47291$	$(3,a+1), (5,a+2), (2)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B	$16$	\( 2^{3} \cdot 3 \)	$1$	$0.647145070$	2.224465009	\( \frac{4102915888729}{9000000} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -8338\) , \( -295969\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2-8338{x}-295969$
60.1-c6	60.1-c	$8$	$12$	\(\Q(\sqrt{-195}) \)	$2$	$[0, 1]$	60.1	\( 2^{2} \cdot 3 \cdot 5 \)	\( 2^{12} \cdot 3^{16} \cdot 5^{12} \)	$3.47291$	$(3,a+1), (5,a+2), (2)$	$1$	$\Z/2\Z\oplus\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$4$	\( 2^{4} \cdot 3^{2} \)	$4.033098199$	$0.647145070$	2.990495275	\( \frac{4102915888729}{9000000} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -3002\) , \( 63929\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-{x}^2-3002{x}+63929$
60.1-d6	60.1-d	$8$	$12$	\(\Q(\sqrt{-195}) \)	$2$	$[0, 1]$	60.1	\( 2^{2} \cdot 3 \cdot 5 \)	\( 2^{12} \cdot 3^{4} \cdot 5^{12} \)	$3.47291$	$(3,a+1), (5,a+2), (2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$4$	\( 2^{4} \cdot 3 \)	$2.281891066$	$0.647145070$	5.075986833	\( \frac{4102915888729}{9000000} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-334{x}-2368$

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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.