Elliptic curves over \(\Q(\sqrt{-2483}) \)

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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
4.1-a1	4.1-a	$2$	$5$	\(\Q(\sqrt{-2483}) \)	$2$	$[0, 1]$	4.1	\( 2^{2} \)	\( 2^{30} \cdot 37^{12} \)	$6.29712$	$(2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3, 5$	3Ns, 5B	$9$	\( 1 \)	$6.146500589$	$3.948517302$	8.766901324	\( -\frac{1680914269}{32768} \)	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -1187 a - 3864\) , \( -29575 a + 855964\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-1187a-3864\right){x}-29575a+855964$
4.1-a2	4.1-a	$2$	$5$	\(\Q(\sqrt{-2483}) \)	$2$	$[0, 1]$	4.1	\( 2^{2} \)	\( 2^{6} \cdot 37^{12} \)	$6.29712$	$(2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3, 5$	3Ns, 5B	$9$	\( 1 \)	$1.229300117$	$19.74258651$	8.766901324	\( \frac{1331}{8} \)	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 88 a + 8236\) , \( -2358 a - 135182\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(88a+8236\right){x}-2358a-135182$
4.1-b1	4.1-b	$2$	$5$	\(\Q(\sqrt{-2483}) \)	$2$	$[0, 1]$	4.1	\( 2^{2} \)	\( 2^{30} \cdot 37^{12} \)	$6.29712$	$(2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3, 5$	3Ns, 5B	$9$	\( 1 \)	$6.146500589$	$3.948517302$	8.766901324	\( -\frac{1680914269}{32768} \)	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 1185 a - 5050\) , \( 29574 a + 826390\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(1185a-5050\right){x}+29574a+826390$
4.1-b2	4.1-b	$2$	$5$	\(\Q(\sqrt{-2483}) \)	$2$	$[0, 1]$	4.1	\( 2^{2} \)	\( 2^{6} \cdot 37^{12} \)	$6.29712$	$(2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3, 5$	3Ns, 5B	$9$	\( 1 \)	$1.229300117$	$19.74258651$	8.766901324	\( \frac{1331}{8} \)	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -90 a + 8325\) , \( 2357 a - 137539\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(-90a+8325\right){x}+2357a-137539$

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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.