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
96.4-d1	96.4-d	$2$	$2$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.4	\( 2^{5} \cdot 3 \)	\( - 2^{8} \cdot 3 \)	$2.11176$	$(a-4), (a+3), (4a+13)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$18.75454831$	2.484100608	\( -\frac{31759}{48} a + \frac{135557}{48} \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 749 a - 3204\) , \( -17453 a + 74611\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(749a-3204\right){x}-17453a+74611$
96.4-g1	96.4-g	$2$	$2$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.4	\( 2^{5} \cdot 3 \)	\( - 2^{8} \cdot 3 \)	$2.11176$	$(a-4), (a+3), (4a+13)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$1$	$25.79187584$	1.708108705	\( -\frac{31759}{48} a + \frac{135557}{48} \)	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 4 a + 16\) , \( 7 a + 22\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+16\right){x}+7a+22$
192.3-a1	192.3-a	$2$	$2$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.3	\( 2^{6} \cdot 3 \)	\( - 2^{20} \cdot 3 \)	$2.51132$	$(a-4), (a+3), (4a+13)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \cdot 3 \)	$0.467633991$	$12.89593792$	4.792618154	\( -\frac{31759}{48} a + \frac{135557}{48} \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -124 a - 400\) , \( 28801 a + 94318\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-124a-400\right){x}+28801a+94318$
192.3-g1	192.3-g	$2$	$2$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.3	\( 2^{6} \cdot 3 \)	\( - 2^{20} \cdot 3 \)	$2.51132$	$(a-4), (a+3), (4a+13)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$9.377274155$	1.242050304	\( -\frac{31759}{48} a + \frac{135557}{48} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 23 a - 98\) , \( -102 a + 436\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\left(23a-98\right){x}-102a+436$

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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.