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
15.1-a2	15.1-a	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 3^{2} \cdot 5^{2} \)	$1.92642$	$(3,a), (a+5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$1$	$31.38702211$	2.865230004	\( -\frac{1}{15} \)	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -4 a + 17\) , \( 175 a + 1001\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4a+17\right){x}+175a+1001$
15.1-b2	15.1-b	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)	$1.92642$	$(3,a), (a+5)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$4$	\( 2^{2} \)	$1$	$10.19195692$	0.930394118	\( -\frac{1}{15} \)	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 1763 a - 9671\) , \( 15245718 a - 83504244\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1763a-9671\right){x}+15245718a-83504244$
15.1-c2	15.1-c	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)	$1.92642$	$(3,a), (a+5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$2.148891872$	$10.19195692$	3.998632720	\( -\frac{1}{15} \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2 a + 14\) , \( 1448 a - 7930\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+14\right){x}+1448a-7930$
15.1-d2	15.1-d	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 3^{2} \cdot 5^{2} \)	$1.92642$	$(3,a), (a+5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{2} \)	$1.259224764$	$31.38702211$	1.803984289	\( -\frac{1}{15} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$

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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.