Elliptic curve search results

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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
50.2-a1	50.2-a	$4$	$15$	3.3.148.1	$3$	$[3, 0]$	50.2	\( 2 \cdot 5^{2} \)	\( - 2 \cdot 5^{10} \)	$2.08656$	$(a^2-a-2), (a^2-a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B.1.2	$25$	\( 1 \)	$1$	$0.730004430$	1.500149864	\( -\frac{1107768943243}{2} a^{2} + 1374213611122 a - \frac{747838372025}{2} \)	\( \bigl[a^{2} - a - 1\) , \( a^{2} - 2 a - 3\) , \( a + 1\) , \( -278324 a^{2} - 325657 a + 128257\) , \( -147052523 a^{2} - 172064153 a + 67763432\bigr] \)	${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-278324a^{2}-325657a+128257\right){x}-147052523a^{2}-172064153a+67763432$
50.2-b1	50.2-b	$4$	$15$	3.3.148.1	$3$	$[3, 0]$	50.2	\( 2 \cdot 5^{2} \)	\( - 2 \cdot 5^{4} \)	$2.08656$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B.1.1, 5B.4.2	$1$	\( 3 \)	$1$	$26.29060985$	0.720358272	\( -\frac{1107768943243}{2} a^{2} + 1374213611122 a - \frac{747838372025}{2} \)	\( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( a\) , \( -553247 a^{2} - 647342 a + 254946\) , \( -412677190 a^{2} - 482868003 a + 190166243\bigr] \)	${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-553247a^{2}-647342a+254946\right){x}-412677190a^{2}-482868003a+190166243$
400.2-d3	400.2-d	$4$	$15$	3.3.148.1	$3$	$[3, 0]$	400.2	\( 2^{4} \cdot 5^{2} \)	\( - 2^{13} \cdot 5^{4} \)	$2.95084$	$(a^2-a-2), (a^2-a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B.4.2	$1$	\( 2 \)	$1$	$8.561511994$	1.407503901	\( -\frac{1107768943243}{2} a^{2} + 1374213611122 a - \frac{747838372025}{2} \)	\( \bigl[a + 1\) , \( a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( -343232 a^{2} - 401611 a + 158168\) , \( 201545807 a^{2} + 235826025 a - 92874552\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2a-2\right){x}^{2}+\left(-343232a^{2}-401611a+158168\right){x}+201545807a^{2}+235826025a-92874552$
400.2-i1	400.2-i	$4$	$15$	3.3.148.1	$3$	$[3, 0]$	400.2	\( 2^{4} \cdot 5^{2} \)	\( - 2^{13} \cdot 5^{10} \)	$2.95084$	$(a^2-a-2), (a^2-a-1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3, 5$	3B, 5B.4.2	$1$	\( 2^{2} \)	$0.120274033$	$20.14349906$	2.389775890	\( -\frac{1107768943243}{2} a^{2} + 1374213611122 a - \frac{747838372025}{2} \)	\( \bigl[a + 1\) , \( a^{2} - a - 1\) , \( a^{2} - 1\) , \( -3829352 a^{2} - 4480664 a + 1764606\) , \( 7509290462 a^{2} + 8786519286 a - 3460364600\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-3829352a^{2}-4480664a+1764606\right){x}+7509290462a^{2}+8786519286a-3460364600$

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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.