Elliptic curve search results

Results (5 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
98.1-a11	98.1-a	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	98.1	\( 2 \cdot 7^{2} \)	\( 2 \cdot 7^{5} \)	$0.79523$	$(a), (-2a+1), (2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3B.1.1	$1$	\( 2^{2} \)	$1$	$17.66572176$	0.693975091	\( \frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -55 a - 91\) , \( 290 a + 416\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-55a-91\right){x}+290a+416$
686.1-d11	686.1-d	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	686.1	\( 2 \cdot 7^{3} \)	\( 2 \cdot 7^{11} \)	$1.29349$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$4$	\( 2^{2} \)	$1$	$1.488944592$	2.105685636	\( \frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \)	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 485 a - 759\) , \( -2705 a + 3591\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(485a-759\right){x}-2705a+3591$
686.2-d11	686.2-d	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	686.2	\( 2 \cdot 7^{3} \)	\( 2 \cdot 7^{11} \)	$1.29349$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$1$	$5.955778371$	2.105685636	\( \frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -134 a - 376\) , \( 1907 a + 2353\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-134a-376\right){x}+1907a+2353$
784.1-a11	784.1-a	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	784.1	\( 2^{4} \cdot 7^{2} \)	\( 2^{13} \cdot 7^{5} \)	$1.33740$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	\( 2^{3} \)	$1$	$1.756927026$	1.242335014	\( \frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -220 a - 362\) , \( -2320 a - 3330\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-220a-362\right){x}-2320a-3330$
4802.1-z11	4802.1-z	$12$	$36$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	4802.1	\( 2 \cdot 7^{4} \)	\( 2 \cdot 7^{17} \)	$2.10397$	$(a), (-2a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$1$	$0.501979150$	0.709905722	\( \frac{2928743223192875}{4802} a + \frac{2070934198465000}{2401} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( -2695 a - 4435\) , \( -102165 a - 147209\bigr] \)	${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-2695a-4435\right){x}-102165a-147209$

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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.