Elliptic curve search results

Results (7 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
49.3-CMa1	49.3-CMa	$1$	$1$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	49.3	\( 7^{2} \)	\( 7^{6} \)	$1.03054$	$(a-2)$	0	$\mathsf{trivial}$	$\textsf{yes}$	$-19$	$\mathrm{U}(1)$	✓			✓	$7$	7Cs.2.1	$1$	\( 1 \)	$1$	$3.318662149$	1.522706625	\( -884736 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -6 a - 2\) , \( -9 a + 9\bigr] \)	${y}^2+{y}={x}^3+\left(-6a-2\right){x}-9a+9$
361.1-CMa1	361.1-CMa	$1$	$1$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	361.1	\( 19^{2} \)	\( 19^{6} \)	$1.69782$	$(-2a+1)$	$2$	$\mathsf{trivial}$	$\textsf{yes}$	$-19$	$\mathrm{U}(1)$	✓	✓		✓	$19$	19B.1.17[2]	$1$	\( 2^{2} \)	$0.156116687$	$2.014351525$	2.308648247	\( -884736 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -38\) , \( 90\bigr] \)	${y}^2+{y}={x}^3-38{x}+90$
3025.7-CMa1	3025.7-CMa	$1$	$1$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	3025.7	\( 5^{2} \cdot 11^{2} \)	\( 5^{6} \cdot 11^{6} \)	$2.88866$	$(a-1), (a+2)$	0	$\mathsf{trivial}$	$\textsf{yes}$	$-19$	$\mathrm{U}(1)$	✓			✓			$9$	\( 1 \)	$1$	$1.183942790$	4.889071875	\( -884736 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -48 a + 58\) , \( -63 a + 454\bigr] \)	${y}^2+{y}={x}^3+\left(-48a+58\right){x}-63a+454$
3025.9-CMa1	3025.9-CMa	$1$	$1$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	3025.9	\( 5^{2} \cdot 11^{2} \)	\( 5^{6} \cdot 11^{6} \)	$2.88866$	$(a-1), (a-3)$	0	$\mathsf{trivial}$	$\textsf{yes}$	$-19$	$\mathrm{U}(1)$	✓			✓			$1$	\( 1 \)	$1$	$1.183942790$	0.543230208	\( -884736 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 42 a - 82\) , \( -203 a + 144\bigr] \)	${y}^2+{y}={x}^3+\left(42a-82\right){x}-203a+144$
3969.3-CMa1	3969.3-CMa	$1$	$1$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	3969.3	\( 3^{4} \cdot 7^{2} \)	\( 3^{12} \cdot 7^{6} \)	$3.09162$	$(a-2), (3)$	0	$\mathsf{trivial}$	$\textsf{yes}$	$-19$	$\mathrm{U}(1)$	✓			✓			$1$	\( 2^{2} \)	$1$	$1.106220716$	2.030275500	\( -884736 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -54 a - 18\) , \( 243 a - 250\bigr] \)	${y}^2+{y}={x}^3+\left(-54a-18\right){x}+243a-250$
6400.3-CMb1	6400.3-CMb	$1$	$1$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	6400.3	\( 2^{8} \cdot 5^{2} \)	\( 2^{24} \cdot 5^{6} \)	$3.48386$	$(a-1), (2)$	0	$\mathsf{trivial}$	$\textsf{yes}$	$-19$	$\mathrm{U}(1)$	✓			✓			$9$	\( 1 \)	$1$	$0.981673502$	4.053804246	\( -884736 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -32 a - 128\) , \( -224 a - 496\bigr] \)	${y}^2={x}^3+\left(-32a-128\right){x}-224a-496$
6400.3-CMa1	6400.3-CMa	$1$	$1$	\(\Q(\sqrt{-19}) \)	$2$	$[0, 1]$	6400.3	\( 2^{8} \cdot 5^{2} \)	\( 2^{24} \cdot 5^{6} \)	$3.48386$	$(a-1), (2)$	0	$\mathsf{trivial}$	$\textsf{yes}$	$-19$	$\mathrm{U}(1)$	✓			✓			$1$	\( 1 \)	$1$	$0.981673502$	0.450422694	\( -884736 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -32 a - 128\) , \( 224 a + 496\bigr] \)	${y}^2={x}^3+\left(-32a-128\right){x}+224a+496$

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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.