Elliptic curve search results

Results (7 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
225.2-a8	225.2-a	$8$	$16$	\(\Q(\sqrt{-31}) \)	$2$	$[0, 1]$	225.2	\( 3^{2} \cdot 5^{2} \)	\( 3^{8} \cdot 5^{2} \)	$1.92693$	$(5,a+1), (5,a+3), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$4$	\( 2^{2} \)	$1$	$0.558925428$	0.803087762	\( \frac{1114544804970241}{405} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$
45.2-a8	45.2-a	$8$	$16$	\(\Q(\sqrt{-155}) \)	$2$	$[0, 1]$	45.2	\( 3^{2} \cdot 5 \)	\( 3^{8} \cdot 5^{14} \)	$2.88143$	$(3,a), (3,a+2), (5,a+2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{5} \)	$1$	$0.558925428$	2.873214126	\( \frac{1114544804970241}{405} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-54001{x}-4834477$
75.1-c8	75.1-c	$8$	$16$	\(\Q(\sqrt{-93}) \)	$2$	$[0, 1]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{20} \cdot 5^{2} \)	$5.07195$	$(3,a), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{3} \)	$5.201251375$	$0.558925428$	4.823254967	\( \frac{1114544804970241}{405} \)	\( \bigl[a\) , \( 0\) , \( 0\) , \( -19260\) , \( -893079\bigr] \)	${y}^2+a{x}{y}={x}^3-19260{x}-893079$
75.2-d8	75.2-d	$8$	$16$	\(\Q(\sqrt{-651}) \)	$2$	$[0, 1]$	75.2	\( 3 \cdot 5^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 13^{12} \)	$6.70956$	$(3,a+1), (5,a+1), (5,a+3)$	$0 \le r \le 2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$64$	\( 2^{3} \)	$1$	$1.117850856$	5.607939751	\( \frac{1114544804970241}{405} \)	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -10849 a + 343932\) , \( -5220402 a - 47503302\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-10849a+343932\right){x}-5220402a-47503302$
75.2-b8	75.2-b	$8$	$16$	\(\Q(\sqrt{-186}) \)	$2$	$[0, 1]$	75.2	\( 3 \cdot 5^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 31^{12} \)	$7.17283$	$(3,a), (5,a+2), (5,a+3)$	$0 \le r \le 2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$64$	\( 2^{3} \)	$1$	$1.117850856$	5.245747299	\( \frac{1114544804970241}{405} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( -2075780\) , \( 1150945707\bigr] \)	${y}^2+{x}{y}={x}^3-2075780{x}+1150945707$
15.1-d8	15.1-d	$8$	$16$	\(\Q(\sqrt{-465}) \)	$2$	$[0, 1]$	15.1	\( 3 \cdot 5 \)	\( 3^{8} \cdot 5^{2} \cdot 31^{12} \)	$7.58434$	$(3,a), (5,a)$	$1 \le r \le 3$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{4} \)	$9.603901418$	$1.117850856$	7.965720493	\( \frac{1114544804970241}{405} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( -2075780\) , \( 1150945707\bigr] \)	${y}^2+{x}{y}={x}^3-2075780{x}+1150945707$
75.1-a8	75.1-a	$8$	$16$	\(\Q(\sqrt{93}) \)	$2$	$[2, 0]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{8} \cdot 5^{2} \)	$2.53598$	$(a+4), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{3} \)	$1$	$10.19195692$	2.113713401	\( \frac{1114544804970241}{405} \)	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -187924 a - 812156\) , \( 97324808 a + 420620839\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-187924a-812156\right){x}+97324808a+420620839$

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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.