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
300.3-e2	300.3-e	$2$	$5$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	300.3	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( - 2^{10} \cdot 3^{3} \cdot 5^{10} \)	$1.70423$	$(-a+2), (-a), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$5$	5B.4.2	$1$	\( 1 \)	$1$	$3.788201406$	0.826653318	\( \frac{1073840073184957}{288} a + \frac{1923556673230885}{288} \)	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -48 a - 233\) , \( -8908 a + 26872\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-48a-233\right){x}-8908a+26872$
300.3-p2	300.3-p	$2$	$5$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	300.3	\( 2^{2} \cdot 3 \cdot 5^{2} \)	\( - 2^{10} \cdot 3^{3} \cdot 5^{10} \)	$1.70423$	$(-a+2), (-a), (2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$5$	5B.1.2	$1$	\( 3 \)	$5.045500216$	$0.440016500$	2.906797612	\( \frac{1073840073184957}{288} a + \frac{1923556673230885}{288} \)	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1879 a - 3373\) , \( -65922 a - 118478\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1879a-3373\right){x}-65922a-118478$
900.2-h2	900.2-h	$2$	$5$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	900.2	\( 2^{2} \cdot 3^{2} \cdot 5^{2} \)	\( - 2^{10} \cdot 3^{9} \cdot 5^{10} \)	$2.24289$	$(-a+2), (-a), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$5$	5B.4.2	$1$	\( 2^{2} \cdot 5 \)	$1$	$0.451013524$	1.968384397	\( \frac{1073840073184957}{288} a + \frac{1923556673230885}{288} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( 410 a - 1383\) , \( -508722 a + 1418527\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(410a-1383\right){x}-508722a+1418527$
900.2-t2	900.2-t	$2$	$5$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	900.2	\( 2^{2} \cdot 3^{2} \cdot 5^{2} \)	\( - 2^{10} \cdot 3^{9} \cdot 5^{10} \)	$2.24289$	$(-a+2), (-a), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$5$	5B.4.2	$1$	\( 2 \cdot 5 \)	$1$	$1.231944671$	2.688323670	\( \frac{1073840073184957}{288} a + \frac{1923556673230885}{288} \)	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -1158 a - 2163\) , \( 38522 a + 47731\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1158a-2163\right){x}+38522a+47731$

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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.