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-a6	15.1-a	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 3^{16} \cdot 5^{4} \)	$1.92642$	$(3,a), (a+5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{6} \)	$1$	$1.961688882$	2.865230004	\( \frac{272223782641}{164025} \)	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -5944 a - 32518\) , \( -592970 a - 3247789\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-5944a-32518\right){x}-592970a-3247789$
15.1-b6	15.1-b	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 2^{12} \cdot 3^{16} \cdot 5^{4} \)	$1.92642$	$(3,a), (a+5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{2} \)	$1$	$10.19195692$	0.930394118	\( \frac{272223782641}{164025} \)	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 11454083 a - 62736611\) , \( -49312315902 a + 270094677816\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11454083a-62736611\right){x}-49312315902a+270094677816$
15.1-c6	15.1-c	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 2^{12} \cdot 3^{16} \cdot 5^{4} \)	$1.92642$	$(3,a), (a+5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{5} \)	$1.074445936$	$10.19195692$	3.998632720	\( \frac{272223782641}{164025} \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 23758 a - 130126\) , \( -4553632 a + 24941270\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(23758a-130126\right){x}-4553632a+24941270$
15.1-d6	15.1-d	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 3^{16} \cdot 5^{4} \)	$1.92642$	$(3,a), (a+5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{3} \)	$2.518449529$	$1.961688882$	1.803984289	\( \frac{272223782641}{164025} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$

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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.