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
19.1-a2	19.1-a	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	19.1	\( 19 \)	\( - 19^{6} \)	$1.77580$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	\( 2 \cdot 3 \)	$1$	$5.486707401$	0.676506855	\( \frac{15636831814539296}{47045881} a^{2} - \frac{38648046941482112}{47045881} a + \frac{10231591814174352}{47045881} \)	\( \bigl[a^{2} - a - 2\) , \( -1\) , \( a\) , \( -24578 a^{2} - 28759 a + 11326\) , \( -2418130 a^{2} - 2829421 a + 1114301\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-24578a^{2}-28759a+11326\right){x}-2418130a^{2}-2829421a+1114301$
304.1-e2	304.1-e	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	304.1	\( 2^{4} \cdot 19 \)	\( - 2^{12} \cdot 19^{6} \)	$2.81891$	$(a^2-a-2), (-a^2-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2 \)	$1.580172787$	$11.35659224$	2.212651479	\( \frac{15636831814539296}{47045881} a^{2} - \frac{38648046941482112}{47045881} a + \frac{10231591814174352}{47045881} \)	\( \bigl[a^{2} - 1\) , \( a + 1\) , \( a^{2} - 1\) , \( -287 a^{2} - 316 a + 124\) , \( 2389 a^{2} + 2745 a - 1088\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-287a^{2}-316a+124\right){x}+2389a^{2}+2745a-1088$
361.2-c2	361.2-c	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( - 19^{12} \)	$2.90082$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$9$	\( 2^{2} \)	$1$	$1.523154399$	1.126822683	\( \frac{15636831814539296}{47045881} a^{2} - \frac{38648046941482112}{47045881} a + \frac{10231591814174352}{47045881} \)	\( \bigl[a^{2} - a - 2\) , \( a - 1\) , \( a^{2} - a - 1\) , \( -44144 a^{2} - 51650 a + 20338\) , \( 5820525 a^{2} + 6810519 a - 2682165\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-44144a^{2}-51650a+20338\right){x}+5820525a^{2}+6810519a-2682165$
475.2-b2	475.2-b	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	475.2	\( 5^{2} \cdot 19 \)	\( - 5^{6} \cdot 19^{6} \)	$3.03658$	$(a^2-a-1), (-a^2-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$0.206686216$	$41.66829336$	2.123770703	\( \frac{15636831814539296}{47045881} a^{2} - \frac{38648046941482112}{47045881} a + \frac{10231591814174352}{47045881} \)	\( \bigl[a^{2} - a - 2\) , \( -a - 1\) , \( a^{2} - a - 1\) , \( -274212 a^{2} - 320850 a + 126358\) , \( -90112799 a^{2} - 105439768 a + 41524980\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-274212a^{2}-320850a+126358\right){x}-90112799a^{2}-105439768a+41524980$

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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.