Elliptic curves over \(\Q(\sqrt{413}) \)

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
4.1-a1	4.1-a	$1$	$1$	\(\Q(\sqrt{413}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( 2^{6} \)	$2.56820$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3$	3Ns	$1$	\( 1 \)	$1$	$18.13499714$	0.892364871	\( -\frac{42875}{8} \)	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 10 a + 172\) , \( 41 a + 617\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(10a+172\right){x}+41a+617$
4.1-b1	4.1-b	$1$	$1$	\(\Q(\sqrt{413}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( 2^{24} \)	$2.56820$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3$	3Ns	$1$	\( 2 \)	$1$	$6.938340258$	0.682826808	\( \frac{2352637}{4096} \)	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 20 a + 273\) , \( 212 a + 2274\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(20a+273\right){x}+212a+2274$
4.1-c1	4.1-c	$1$	$1$	\(\Q(\sqrt{413}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( 2^{6} \)	$2.56820$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3$	3Ns	$1$	\( 1 \)	$1$	$18.13499714$	0.892364871	\( -\frac{42875}{8} \)	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -12 a + 183\) , \( -42 a + 658\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a+183\right){x}-42a+658$
4.1-d1	4.1-d	$1$	$1$	\(\Q(\sqrt{413}) \)	$2$	$[2, 0]$	4.1	\( 2^{2} \)	\( 2^{24} \)	$2.56820$	$(2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3$	3Ns	$1$	\( 2 \)	$1$	$6.938340258$	0.682826808	\( \frac{2352637}{4096} \)	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -22 a + 295\) , \( -213 a + 2487\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-22a+295\right){x}-213a+2487$

 

  *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.