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
26.1-a2	26.1-a	$2$	$3$	3.3.148.1	$3$	$[3, 0]$	26.1	\( 2 \cdot 13 \)	\( - 2^{3} \cdot 13^{3} \)	$1.87111$	$(a^2-a-2), (a^2-2a-2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.2	$1$	\( 3 \)	$1$	$3.099895835$	0.764429604	\( -\frac{936828579535}{4394} a^{2} + \frac{1669497916531}{4394} a - \frac{428712816945}{4394} \)	\( \bigl[1\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( -26 a^{2} - 25 a + 19\) , \( -93 a^{2} - 111 a + 36\bigr] \)	${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-26a^{2}-25a+19\right){x}-93a^{2}-111a+36$
208.1-b1	208.1-b	$2$	$3$	3.3.148.1	$3$	$[3, 0]$	208.1	\( 2^{4} \cdot 13 \)	\( - 2^{15} \cdot 13^{3} \)	$2.64614$	$(a^2-a-2), (a^2-2a-2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2^{2} \)	$0.027494208$	$63.63376441$	1.725755341	\( -\frac{936828579535}{4394} a^{2} + \frac{1669497916531}{4394} a - \frac{428712816945}{4394} \)	\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 1\) , \( a^{2} - a - 2\) , \( -443 a^{2} + 1079 a - 295\) , \( 8550 a^{2} - 21172 a + 5758\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-443a^{2}+1079a-295\right){x}+8550a^{2}-21172a+5758$
338.2-c2	338.2-c	$2$	$3$	3.3.148.1	$3$	$[3, 0]$	338.2	\( 2 \cdot 13^{2} \)	\( - 2^{3} \cdot 13^{9} \)	$2.86917$	$(a^2-a-2), (a^2-2a-2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2 \cdot 3 \)	$1$	$5.652076451$	2.787586934	\( -\frac{936828579535}{4394} a^{2} + \frac{1669497916531}{4394} a - \frac{428712816945}{4394} \)	\( \bigl[a^{2} - a - 1\) , \( -a^{2} + 2\) , \( a^{2} - a - 1\) , \( -75 a^{2} - 55 a + 52\) , \( 512 a^{2} + 659 a - 222\bigr] \)	${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-75a^{2}-55a+52\right){x}+512a^{2}+659a-222$

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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.