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
96.6-d1	96.6-d	$1$	$1$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.6	\( 2^{5} \cdot 3 \)	\( 2^{12} \cdot 3^{2} \)	$2.11176$	$(a+3), (4a+13)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2^{2} \)	$1$	$2.631200657$	1.394044163	\( -\frac{62998269440}{3} a - 68771386368 \)	\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -1340 a - 4385\) , \( -49989 a - 163710\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-1340a-4385\right){x}-49989a-163710$
96.6-f1	96.6-f	$1$	$1$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.6	\( 2^{5} \cdot 3 \)	\( 2^{12} \cdot 3^{2} \)	$2.11176$	$(a+3), (4a+13)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2^{2} \)	$1$	$7.072896391$	3.747312051	\( -\frac{62998269440}{3} a - 68771386368 \)	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( 2246 a - 9598\) , \( 122571 a - 523989\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2246a-9598\right){x}+122571a-523989$
192.6-k1	192.6-k	$1$	$1$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.6	\( 2^{6} \cdot 3 \)	\( 2^{6} \cdot 3^{2} \)	$2.51132$	$(a+3), (4a+13)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2 \)	$0.522611832$	$30.54628654$	8.457854761	\( -\frac{62998269440}{3} a - 68771386368 \)	\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 29722 a - 127053\) , \( -5712610 a + 24420925\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(29722a-127053\right){x}-5712610a+24420925$
192.6-s1	192.6-s	$1$	$1$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.6	\( 2^{6} \cdot 3 \)	\( 2^{6} \cdot 3^{2} \)	$2.51132$	$(a+3), (4a+13)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2 \)	$1$	$1.218492441$	0.322786533	\( -\frac{62998269440}{3} a - 68771386368 \)	\( \bigl[0\) , \( -1\) , \( a + 1\) , \( -25 a - 84\) , \( -127 a - 418\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-25a-84\right){x}-127a-418$

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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.