Elliptic curves over \(\Q(\sqrt{485}) \)

Results (6 matches)

 

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
1.1-a1	1.1-a	$1$	$1$	\(\Q(\sqrt{485}) \)	$2$	$[2, 0]$	1.1	\( 1 \)	\( 1 \)	$1.96793$	$\textsf{none}$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$2, 3$	2Cn, 3Nn	$1$	\( 1 \)	$1$	$76.38421279$	3.468428434	\( 32768 \)	\( \bigl[0\) , \( a\) , \( 1\) , \( 59 a - 635\) , \( -991 a + 11464\bigr] \)	${y}^2+{y}={x}^{3}+a{x}^{2}+\left(59a-635\right){x}-991a+11464$
1.1-b1	1.1-b	$1$	$1$	\(\Q(\sqrt{485}) \)	$2$	$[2, 0]$	1.1	\( 1 \)	\( 5^{12} \)	$1.96793$	$\textsf{none}$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$2, 3$	2Cn, 3Nn	$1$	\( 1 \)	$1$	$76.38421279$	3.468428434	\( 32768 \)	\( \bigl[0\) , \( -a\) , \( 1\) , \( 1467 a - 16843\) , \( -93611 a + 1077533\bigr] \)	${y}^2+{y}={x}^{3}-a{x}^{2}+\left(1467a-16843\right){x}-93611a+1077533$
4.1-a1	4.1-a	$1$	$1$	\(\Q(\sqrt{485}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( - 2^{6} \cdot 5^{12} \)	$2.78307$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3Nn	$1$	\( 1 \)	$1$	$14.90424802$	0.676767040	\( \frac{81789869}{4} a + \frac{1718536973}{8} \)	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -1596 a - 16735\) , \( -120876 a - 1270619\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1596a-16735\right){x}-120876a-1270619$
4.1-b1	4.1-b	$1$	$1$	\(\Q(\sqrt{485}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( - 2^{6} \)	$2.78307$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3Nn	$1$	\( 1 \)	$1$	$14.90424802$	0.676767040	\( \frac{81789869}{4} a + \frac{1718536973}{8} \)	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -63 a - 631\) , \( -665 a - 6956\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-63a-631\right){x}-665a-6956$
4.1-c1	4.1-c	$1$	$1$	\(\Q(\sqrt{485}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( - 2^{6} \cdot 5^{12} \)	$2.78307$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3Nn	$1$	\( 1 \)	$1$	$14.90424802$	0.676767040	\( -\frac{81789869}{4} a + \frac{1882116711}{8} \)	\( \bigl[1\) , \( -a\) , \( 0\) , \( 1596 a - 18331\) , \( 120876 a - 1391495\bigr] \)	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(1596a-18331\right){x}+120876a-1391495$
4.1-d1	4.1-d	$1$	$1$	\(\Q(\sqrt{485}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( - 2^{6} \)	$2.78307$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3Nn	$1$	\( 1 \)	$1$	$14.90424802$	0.676767040	\( -\frac{81789869}{4} a + \frac{1882116711}{8} \)	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 65 a - 694\) , \( 729 a - 8315\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(65a-694\right){x}+729a-8315$

 

  *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.