Elliptic curves over \(\Q(\sqrt{-95}) \) of conductor 576.11

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 1000 over imaginary quadratic fields with absolute discriminant 95

Note: The completeness Only modular elliptic curves are included

Results (16 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
576.11-a1	576.11-a	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{22} \cdot 3^{16} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$9.104725372$	$0.908836754$	3.395868945	\( \frac{207646}{6561} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \)	${y}^2={x}^3-{x}^2+16{x}-180$
576.11-a2	576.11-a	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{2} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$4.552362686$	$7.270694035$	3.395868945	\( \frac{2048}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)	${y}^2={x}^3-{x}^2+{x}$
576.11-a3	576.11-a	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{4} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{6} \)	$2.276181343$	$3.635347017$	3.395868945	\( \frac{35152}{9} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \)	${y}^2={x}^3-{x}^2-4{x}+4$
576.11-a4	576.11-a	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{8} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{4} \)	$4.552362686$	$1.817673508$	3.395868945	\( \frac{1556068}{81} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \)	${y}^2={x}^3-{x}^2-24{x}-36$
576.11-a5	576.11-a	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{2} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$4.552362686$	$1.817673508$	3.395868945	\( \frac{28756228}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \)	${y}^2={x}^3-{x}^2-64{x}+220$
576.11-a6	576.11-a	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{22} \cdot 3^{4} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$9.104725372$	$0.908836754$	3.395868945	\( \frac{3065617154}{9} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \)	${y}^2={x}^3-{x}^2-384{x}-2772$
576.11-b1	576.11-b	$2$	$2$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{6} \cdot 11^{12} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \cdot 3 \)	$2.527636597$	$2.512968670$	7.820259281	\( \frac{27436}{27} \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -151 a - 128\) , \( 684 a + 4860\bigr] \)	${y}^2={x}^3+\left(-a-1\right){x}^2+\left(-151a-128\right){x}+684a+4860$
576.11-b2	576.11-b	$2$	$2$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{22} \cdot 3^{12} \cdot 11^{12} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \cdot 3 \)	$5.055273194$	$1.256484335$	7.820259281	\( \frac{2060602}{729} \)	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 809 a + 632\) , \( 4196 a + 61324\bigr] \)	${y}^2={x}^3+\left(-a-1\right){x}^2+\left(809a+632\right){x}+4196a+61324$
576.11-c1	576.11-c	$2$	$2$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{6} \cdot 11^{12} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \cdot 3 \)	$2.527636597$	$2.512968670$	7.820259281	\( \frac{27436}{27} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 153 a - 280\) , \( -532 a + 5264\bigr] \)	${y}^2={x}^3+\left(a+1\right){x}^2+\left(153a-280\right){x}-532a+5264$
576.11-c2	576.11-c	$2$	$2$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{22} \cdot 3^{12} \cdot 11^{12} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \cdot 3 \)	$5.055273194$	$1.256484335$	7.820259281	\( \frac{2060602}{729} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -807 a + 1440\) , \( -5004 a + 66960\bigr] \)	${y}^2={x}^3+\left(a+1\right){x}^2+\left(-807a+1440\right){x}-5004a+66960$
576.11-d1	576.11-d	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{22} \cdot 3^{16} \cdot 5^{12} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{6} \)	$1.562595083$	$0.908836754$	9.325035784	\( \frac{207646}{6561} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 392\) , \( -21712\bigr] \)	${y}^2={x}^3+{x}^2+392{x}-21712$
576.11-d2	576.11-d	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{2} \cdot 5^{12} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$3.125190167$	$7.270694035$	9.325035784	\( \frac{2048}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 17\) , \( 38\bigr] \)	${y}^2={x}^3+{x}^2+17{x}+38$
576.11-d3	576.11-d	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{4} \cdot 5^{12} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{4} \)	$6.250380335$	$3.635347017$	9.325035784	\( \frac{35152}{9} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -108\) , \( 288\bigr] \)	${y}^2={x}^3+{x}^2-108{x}+288$
576.11-d4	576.11-d	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{8} \cdot 5^{12} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{6} \)	$3.125190167$	$1.817673508$	9.325035784	\( \frac{1556068}{81} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -608\) , \( -5712\bigr] \)	${y}^2={x}^3+{x}^2-608{x}-5712$
576.11-d5	576.11-d	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{20} \cdot 3^{2} \cdot 5^{12} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$12.50076067$	$1.817673508$	9.325035784	\( \frac{28756228}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1608\) , \( 24288\bigr] \)	${y}^2={x}^3+{x}^2-1608{x}+24288$
576.11-d6	576.11-d	$6$	$8$	\(\Q(\sqrt{-95}) \)	$2$	$[0, 1]$	576.11	\( 2^{6} \cdot 3^{2} \)	\( 2^{22} \cdot 3^{4} \cdot 5^{12} \)	$4.26684$	$(2,a), (2,a+1), (3,a), (3,a+2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{2} \)	$6.250380335$	$0.908836754$	9.325035784	\( \frac{3065617154}{9} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -9608\) , \( -365712\bigr] \)	${y}^2={x}^3+{x}^2-9608{x}-365712$

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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.