Elliptic curves over \(\Q(\sqrt{-299}) \) of conductor 100.2

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 100 over imaginary quadratic fields with absolute discriminant 299

Note: The completeness Only modular elliptic curves are included

Results (4 matches)

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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
100.2-a1	100.2-a	$2$	$2$	\(\Q(\sqrt{-299}) \)	$2$	$[0, 1]$	100.2	\( 2^{2} \cdot 5^{2} \)	\( 2^{12} \cdot 3^{12} \cdot 5^{6} \)	$4.88623$	$(5,a), (5,a+4), (2)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Ns	$1$	\( 2 \cdot 3 \)	$2.409350082$	$3.052416071$	5.103748809	\( \frac{16194277}{8000} \)	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -27 a + 66\) , \( 95 a + 290\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-27a+66\right){x}+95a+290$
100.2-a2	100.2-a	$2$	$2$	\(\Q(\sqrt{-299}) \)	$2$	$[0, 1]$	100.2	\( 2^{2} \cdot 5^{2} \)	\( 2^{6} \cdot 3^{12} \cdot 5^{12} \)	$4.88623$	$(5,a), (5,a+4), (2)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Ns	$1$	\( 2^{2} \cdot 3 \)	$2.409350082$	$1.526208035$	5.103748809	\( \frac{10260751717}{125000} \)	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -67 a + 186\) , \( 271 a + 4298\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-67a+186\right){x}+271a+4298$
100.2-b1	100.2-b	$2$	$2$	\(\Q(\sqrt{-299}) \)	$2$	$[0, 1]$	100.2	\( 2^{2} \cdot 5^{2} \)	\( 2^{12} \cdot 3^{12} \cdot 5^{6} \)	$4.88623$	$(5,a), (5,a+4), (2)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Ns	$1$	\( 2 \cdot 3 \)	$2.409350082$	$3.052416071$	5.103748809	\( \frac{16194277}{8000} \)	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -10 a + 114\) , \( 8 a - 234\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-10a+114\right){x}+8a-234$
100.2-b2	100.2-b	$2$	$2$	\(\Q(\sqrt{-299}) \)	$2$	$[0, 1]$	100.2	\( 2^{2} \cdot 5^{2} \)	\( 2^{6} \cdot 3^{12} \cdot 5^{12} \)	$4.88623$	$(5,a), (5,a+4), (2)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Ns	$1$	\( 2^{2} \cdot 3 \)	$2.409350082$	$1.526208035$	5.103748809	\( \frac{10260751717}{125000} \)	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 30 a + 194\) , \( -48 a + 950\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(30a+194\right){x}-48a+950$

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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.