Elliptic curves over \(\Q(\sqrt{5}) \) of conductor 49.1

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree/signature	Bad \(p\)	$\Q$-curves	Torsion structure	CM
Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image
j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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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-a1	49.1-a	$2$	$5$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	49.1	\( 7^{2} \)	\( 7^{10} \)	$0.52866$	$(7)$	$0$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$5$	5B.1.4[2]	$1$	\( 1 \)	$1$	$1.045448192$	0.467538645	\( -\frac{2887553024}{16807} \)	\( \bigl[0\) , \( -\phi + 1\) , \( 1\) , \( -30 \phi - 29\) , \( -102 \phi - 84\bigr] \)	${y}^2+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-30\phi-29\right){x}-102\phi-84$
49.1-a2	49.1-a	$2$	$5$	\(\Q(\sqrt{5}) \)	$2$	$[2, 0]$	49.1	\( 7^{2} \)	\( 7^{2} \)	$0.52866$	$(7)$	$0$	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$5$	5B.1.1[2]	$1$	\( 1 \)	$1$	$26.13620482$	0.467538645	\( \frac{4096}{7} \)	\( \bigl[0\) , \( \phi\) , \( 1\) , \( 1\) , \( 0\bigr] \)	${y}^2+{y}={x}^{3}+\phi{x}^{2}+{x}$

 

  *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.