Elliptic curves over \(\Q(\sqrt{-313}) \)

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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
2.1-a1	2.1-a	$2$	$5$	\(\Q(\sqrt{-313}) \)	$2$	$[0, 1]$	2.1	\( 2 \)	\( 2^{18} \)	$3.76009$	$(2,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3, 5$	3Nn, 5B	$25$	\( 2 \cdot 3 \)	$1$	$0.974549768$	4.131360733	\( -\frac{7762509612594001}{8} \)	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -27 a + 18658\) , \( -43025 a - 445822\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-27a+18658\right){x}-43025a-445822$
2.1-a2	2.1-a	$2$	$5$	\(\Q(\sqrt{-313}) \)	$2$	$[0, 1]$	2.1	\( 2 \)	\( 2^{42} \)	$3.76009$	$(2,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3, 5$	3Nn, 5B	$1$	\( 2 \cdot 3 \cdot 5 \)	$1$	$4.872748844$	4.131360733	\( -\frac{13997521}{32768} \)	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -27 a + 2178\) , \( 335 a - 17342\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-27a+2178\right){x}+335a-17342$
2.1-b1	2.1-b	$2$	$5$	\(\Q(\sqrt{-313}) \)	$2$	$[0, 1]$	2.1	\( 2 \)	\( 2^{18} \)	$3.76009$	$(2,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3, 5$	3Nn, 5B	$25$	\( 2 \cdot 3 \)	$1$	$0.974549768$	4.131360733	\( -\frac{7762509612594001}{8} \)	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 25 a + 18658\) , \( 43024 a - 445822\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(25a+18658\right){x}+43024a-445822$
2.1-b2	2.1-b	$2$	$5$	\(\Q(\sqrt{-313}) \)	$2$	$[0, 1]$	2.1	\( 2 \)	\( 2^{42} \)	$3.76009$	$(2,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$3, 5$	3Nn, 5B	$1$	\( 2 \cdot 3 \cdot 5 \)	$1$	$4.872748844$	4.131360733	\( -\frac{13997521}{32768} \)	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 25 a + 2178\) , \( -336 a - 17342\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(25a+2178\right){x}-336a-17342$

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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.