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
22500.3-d2	22500.3-d	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	22500.3	\( 2^{2} \cdot 3^{2} \cdot 5^{4} \)	\( 2^{8} \cdot 3^{4} \cdot 5^{6} \)	$2.18884$	$(a+1), (-a-2), (2a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \cdot 3 \)	$0.121183932$	$2.388115705$	3.472815038	\( \frac{131072}{9} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 22\bigr] \)	${y}^2={x}^{3}-{x}^{2}-13{x}+22$
22500.3-e2	22500.3-e	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	22500.3	\( 2^{2} \cdot 3^{2} \cdot 5^{4} \)	\( 2^{8} \cdot 3^{4} \cdot 5^{18} \)	$2.18884$	$(a+1), (-a-2), (2a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$1.928831358$	$0.477623141$	3.685017969	\( \frac{131072}{9} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -333\) , \( 2088\bigr] \)	${y}^2={x}^{3}+{x}^{2}-333{x}+2088$
90000.3-h2	90000.3-h	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	90000.3	\( 2^{4} \cdot 3^{2} \cdot 5^{4} \)	\( 2^{8} \cdot 3^{4} \cdot 5^{12} \)	$3.09549$	$(a+1), (-a-2), (2a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$0.531805779$	$1.067997811$	4.543739270	\( \frac{131072}{9} \)	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 54 i + 40\) , \( 4 i - 189\bigr] \)	${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(54i+40\right){x}+4i-189$
90000.3-i2	90000.3-i	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	90000.3	\( 2^{4} \cdot 3^{2} \cdot 5^{4} \)	\( 2^{8} \cdot 3^{4} \cdot 5^{12} \)	$3.09549$	$(a+1), (-a-2), (2a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$0.531805779$	$1.067997811$	4.543739270	\( \frac{131072}{9} \)	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -54 i + 40\) , \( -4 i - 189\bigr] \)	${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-54i+40\right){x}-4i-189$

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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.