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
81.1-a1	81.1-a	$8$	$30$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	81.1	\( 3^{4} \)	\( 3^{6} \)	$0.59944$	$(3)$	0	$\Z/6\Z$	$\textsf{potential}$	$-15$	$N(\mathrm{U}(1))$	✓			✓	$3$	3B.1.1	$1$	\( 2 \)	$1$	$23.62521625$	0.586973216	\( -85995 a - 52515 \)	\( \bigl[1\) , \( -1\) , \( \phi\) , \( -2 \phi\) , \( \phi\bigr] \)	${y}^2+{x}{y}+\phi{y}={x}^{3}-{x}^{2}-2\phi{x}+\phi$
81.1-a2	81.1-a	$8$	$30$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	81.1	\( 3^{4} \)	\( 3^{18} \)	$0.59944$	$(3)$	0	$\Z/2\Z$	$\textsf{potential}$	$-15$	$N(\mathrm{U}(1))$	✓			✓	$3$	3B.1.2	$1$	\( 2 \)	$1$	$2.625024027$	0.586973216	\( -85995 a - 52515 \)	\( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( -14 \phi - 2\) , \( -21 \phi - 6\bigr] \)	${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(-14\phi-2\right){x}-21\phi-6$
2025.1-e1	2025.1-e	$8$	$30$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	2025.1	\( 3^{4} \cdot 5^{2} \)	\( 3^{6} \cdot 5^{6} \)	$1.34039$	$(-2a+1), (3)$	0	$\Z/2\Z$	$\textsf{potential}$	$-15$	$N(\mathrm{U}(1))$	✓			✓			$1$	\( 2^{2} \)	$1$	$3.521839301$	1.575014416	\( -85995 a - 52515 \)	\( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -6 \phi + 6\) , \( -7 \phi + 10\bigr] \)	${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-6\phi+6\right){x}-7\phi+10$
2025.1-e2	2025.1-e	$8$	$30$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	2025.1	\( 3^{4} \cdot 5^{2} \)	\( 3^{18} \cdot 5^{6} \)	$1.34039$	$(-2a+1), (3)$	0	$\Z/2\Z$	$\textsf{potential}$	$-15$	$N(\mathrm{U}(1))$	✓			✓			$1$	\( 2^{2} \)	$1$	$3.521839301$	1.575014416	\( -85995 a - 52515 \)	\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -59 \phi + 51\) , \( 253 \phi - 264\bigr] \)	${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-59\phi+51\right){x}+253\phi-264$

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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.