Elliptic curve search results

Results (8 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
49.1-a3	49.1-a	$6$	$147$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	49.1	\( 7^{2} \)	\( 7^{8} \)	$1.08342$	$(-a-3)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-147$	$N(\mathrm{U}(1))$	✓			✓	$7$	7Cs.1.2	$1$	\( 1 \)	$1$	$7.676076964$	1.675057320	\( -7604567359488000 a - 13621969096704000 \)	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 281 a - 1608\) , \( -5819 a + 26465\bigr] \)	${y}^2+{y}={x}^3+\left(-a-1\right){x}^2+\left(281a-1608\right){x}-5819a+26465$
49.1-a4	49.1-a	$6$	$147$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	49.1	\( 7^{2} \)	\( 7^{8} \)	$1.08342$	$(-a-3)$	0	$\mathsf{trivial}$	$\textsf{potential}$	$-147$	$N(\mathrm{U}(1))$	✓			✓	$7$	7Cs.1.2	$49$	\( 1 \)	$1$	$0.156654631$	1.675057320	\( -7604567359488000 a - 13621969096704000 \)	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -4129 a - 7488\) , \( -225461 a - 404182\bigr] \)	${y}^2+{y}={x}^3+\left(a+1\right){x}^2+\left(-4129a-7488\right){x}-225461a-404182$
441.1-d3	441.1-d	$6$	$147$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	441.1	\( 3^{2} \cdot 7^{2} \)	\( 3^{6} \cdot 7^{8} \)	$1.87654$	$(a+1), (-a-3)$	$1$	$\Z/3\Z$	$\textsf{potential}$	$-147$	$N(\mathrm{U}(1))$	✓			✓	$3, 7$	3B.1.1, 7Cs.6.2	$1$	\( 2 \cdot 3 \)	$6.259930461$	$1.096582423$	1.997284256	\( -7604567359488000 a - 13621969096704000 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( -2310 a - 5460\) , \( 113190 a + 184203\bigr] \)	${y}^2+{y}={x}^3+\left(-2310a-5460\right){x}+113190a+184203$
441.1-d4	441.1-d	$6$	$147$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	441.1	\( 3^{2} \cdot 7^{2} \)	\( 3^{6} \cdot 7^{8} \)	$1.87654$	$(a+1), (-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{potential}$	$-147$	$N(\mathrm{U}(1))$	✓			✓	$3, 7$	3B.1.1, 7Cs.6.2	$1$	\( 2 \cdot 3 \)	$2.086643487$	$0.365527474$	1.997284256	\( -7604567359488000 a - 13621969096704000 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 6510 a - 18690\) , \( -446292 a + 1241182\bigr] \)	${y}^2+{y}={x}^3+\left(6510a-18690\right){x}-446292a+1241182$
1225.2-c3	1225.2-c	$6$	$147$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1225.2	\( 5^{2} \cdot 7^{2} \)	\( 5^{6} \cdot 7^{2} \)	$2.42260$	$(a), (-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{potential}$	$-147$	$N(\mathrm{U}(1))$	✓			✓	$7$	7Cs.6.2	$1$	\( 2 \)	$3.279019542$	$0.749108406$	2.144070295	\( -7604567359488000 a - 13621969096704000 \)	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -919 a - 1848\) , \( -26136 a - 45656\bigr] \)	${y}^2+{y}={x}^3+\left(a+1\right){x}^2+\left(-919a-1848\right){x}-26136a-45656$
1225.2-c4	1225.2-c	$6$	$147$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1225.2	\( 5^{2} \cdot 7^{2} \)	\( 5^{6} \cdot 7^{2} \)	$2.42260$	$(a), (-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{potential}$	$-147$	$N(\mathrm{U}(1))$	✓			✓	$7$	7Cs.6.2	$1$	\( 2 \)	$1.093006514$	$2.247325220$	2.144070295	\( -7604567359488000 a - 13621969096704000 \)	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 971 a - 2898\) , \( 27140 a - 74487\bigr] \)	${y}^2+{y}={x}^3+\left(-a-1\right){x}^2+\left(971a-2898\right){x}+27140a-74487$
1225.3-c3	1225.3-c	$6$	$147$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1225.3	\( 5^{2} \cdot 7^{2} \)	\( 5^{6} \cdot 7^{2} \)	$2.42260$	$(-a+1), (-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{potential}$	$-147$	$N(\mathrm{U}(1))$	✓			✓	$7$	7Cs.6.2	$1$	\( 2 \)	$1.093006514$	$2.247325220$	2.144070295	\( -7604567359488000 a - 13621969096704000 \)	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 2441 a - 6888\) , \( 100022 a - 279017\bigr] \)	${y}^2+{y}={x}^3+\left(a+1\right){x}^2+\left(2441a-6888\right){x}+100022a-279017$
1225.3-c4	1225.3-c	$6$	$147$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1225.3	\( 5^{2} \cdot 7^{2} \)	\( 5^{6} \cdot 7^{2} \)	$2.42260$	$(-a+1), (-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{potential}$	$-147$	$N(\mathrm{U}(1))$	✓			✓	$7$	7Cs.6.2	$1$	\( 2 \)	$3.279019542$	$0.749108406$	2.144070295	\( -7604567359488000 a - 13621969096704000 \)	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -289 a - 1008\) , \( -6904 a - 8304\bigr] \)	${y}^2+{y}={x}^3+\left(-a-1\right){x}^2+\left(-289a-1008\right){x}-6904a-8304$

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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.