Elliptic curves over \(\Q(\sqrt{82}) \)

Results (4 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
2.1-a1	2.1-a	$2$	$2$	\(\Q(\sqrt{82}) \)	$2$	$[2, 0]$	2.1	\( 2 \)	\( 2^{16} \cdot 3^{12} \)	$1.92457$	$(2,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$4$	\( 2 \)	$1$	$9.868400111$	1.089782484	\( \frac{16974593}{256} \)	\( \bigl[1\) , \( -a\) , \( 1\) , \( -43 a - 364\) , \( -332 a - 2988\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-43a-364\right){x}-332a-2988$
2.1-a2	2.1-a	$2$	$2$	\(\Q(\sqrt{82}) \)	$2$	$[2, 0]$	2.1	\( 2 \)	\( 2^{8} \cdot 3^{12} \)	$1.92457$	$(2,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$16$	\( 2 \)	$1$	$2.467100027$	1.089782484	\( \frac{68769820673}{16} \)	\( \bigl[1\) , \( -a\) , \( 1\) , \( -683 a - 6204\) , \( -27372 a - 248108\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-683a-6204\right){x}-27372a-248108$
2.1-b1	2.1-b	$2$	$2$	\(\Q(\sqrt{82}) \)	$2$	$[2, 0]$	2.1	\( 2 \)	\( 2^{16} \cdot 3^{12} \)	$1.92457$	$(2,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$4$	\( 2 \)	$1$	$9.868400111$	1.089782484	\( \frac{16974593}{256} \)	\( \bigl[1\) , \( a\) , \( 1\) , \( 43 a - 364\) , \( 332 a - 2988\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(43a-364\right){x}+332a-2988$
2.1-b2	2.1-b	$2$	$2$	\(\Q(\sqrt{82}) \)	$2$	$[2, 0]$	2.1	\( 2 \)	\( 2^{8} \cdot 3^{12} \)	$1.92457$	$(2,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$16$	\( 2 \)	$1$	$2.467100027$	1.089782484	\( \frac{68769820673}{16} \)	\( \bigl[1\) , \( a\) , \( 1\) , \( 683 a - 6204\) , \( 27372 a - 248108\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(683a-6204\right){x}+27372a-248108$

 

  *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.