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The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 150000 over imaginary quadratic fields with absolute discriminant 3

Note: The completeness Only modular elliptic curves are included

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Results (26 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
120000.1-a1 120000.1-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.696317377$ 1.608076100 \( \frac{21296}{15} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 92\) , \( -188\bigr] \) ${y}^2={x}^{3}-{x}^{2}+92{x}-188$
120000.1-a2 120000.1-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.348158688$ 1.608076100 \( \frac{470596}{225} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -408\) , \( -1188\bigr] \) ${y}^2={x}^{3}-{x}^{2}-408{x}-1188$
120000.1-a3 120000.1-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.174079344$ 1.608076100 \( \frac{136835858}{1875} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -3408\) , \( 76812\bigr] \) ${y}^2={x}^{3}-{x}^{2}-3408{x}+76812$
120000.1-a4 120000.1-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.174079344$ 1.608076100 \( \frac{546718898}{405} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -5408\) , \( -151188\bigr] \) ${y}^2={x}^{3}-{x}^{2}-5408{x}-151188$
120000.1-b1 120000.1-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.050574661$ $2.657582450$ 4.966370047 \( \frac{5120}{3} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 7\) , \( -3\bigr] \) ${y}^2={x}^{3}-{x}^{2}+7{x}-3$
120000.1-c1 120000.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $7.547184459$ $0.076578751$ 5.338909986 \( -\frac{27995042}{1171875} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -2008\) , \( -295988\bigr] \) ${y}^2={x}^{3}-{x}^{2}-2008{x}-295988$
120000.1-c2 120000.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.886796114$ $0.153157502$ 5.338909986 \( \frac{54607676}{32805} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 1992\) , \( 6012\bigr] \) ${y}^2={x}^{3}-{x}^{2}+1992{x}+6012$
120000.1-c3 120000.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.886796114$ $0.306315004$ 5.338909986 \( \frac{3631696}{2025} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -508\) , \( 1012\bigr] \) ${y}^2={x}^{3}-{x}^{2}-508{x}+1012$
120000.1-c4 120000.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $7.547184459$ $0.153157502$ 5.338909986 \( \frac{868327204}{5625} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -5008\) , \( -133988\bigr] \) ${y}^2={x}^{3}-{x}^{2}-5008{x}-133988$
120000.1-c5 120000.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $2$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.886796114$ $0.612630008$ 5.338909986 \( \frac{24918016}{45} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -383\) , \( 3012\bigr] \) ${y}^2={x}^{3}-{x}^{2}-383{x}+3012$
120000.1-c6 120000.1-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $7.547184459$ $0.076578751$ 5.338909986 \( \frac{1770025017602}{75} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -80008\) , \( -8683988\bigr] \) ${y}^2={x}^{3}-{x}^{2}-80008{x}-8683988$
120000.1-d1 120000.1-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.123833754$ 2.595382882 \( \frac{27436}{27} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 32\) , \( -68\bigr] \) ${y}^2={x}^{3}-{x}^{2}+32{x}-68$
120000.1-d2 120000.1-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.561916877$ 2.595382882 \( \frac{2060602}{729} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -168\) , \( -468\bigr] \) ${y}^2={x}^{3}-{x}^{2}-168{x}-468$
120000.1-e1 120000.1-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.097862287$ 3.616052353 \( -\frac{8780800}{2187} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -5833 a + 5833\) , \( 207037\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-5833a+5833\right){x}+207037$
120000.1-f1 120000.1-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.015833389$ $0.489311437$ 3.005854131 \( -\frac{8780800}{2187} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -233\) , \( 1563\bigr] \) ${y}^2={x}^{3}+{x}^{2}-233{x}+1563$
120000.1-g1 120000.1-g \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.655400181$ $0.224766750$ 5.155676752 \( \frac{27436}{27} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 792 a - 792\) , \( -6912\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(792a-792\right){x}-6912$
120000.1-g2 120000.1-g \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.310800362$ $0.112383375$ 5.155676752 \( \frac{2060602}{729} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -4208 a + 4208\) , \( -66912\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-4208a+4208\right){x}-66912$
120000.1-h1 120000.1-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.331860695$ $0.727069403$ 5.594510179 \( \frac{73696}{3} a - \frac{624368}{3} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 125 a + 142\) , \( -1125 a + 1538\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(125a+142\right){x}-1125a+1538$
120000.1-h2 120000.1-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.331860695$ $0.727069403$ 5.594510179 \( -\frac{73696}{3} a - \frac{550672}{3} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -125 a + 267\) , \( 1125 a + 413\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-125a+267\right){x}+1125a+413$
120000.1-h3 120000.1-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.832965173$ $0.181767350$ 5.594510179 \( \frac{207646}{6561} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 392\) , \( -21712\bigr] \) ${y}^2={x}^{3}+{x}^{2}+392{x}-21712$
120000.1-h4 120000.1-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.665930347$ $1.454138807$ 5.594510179 \( \frac{2048}{3} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 17\) , \( 38\bigr] \) ${y}^2={x}^{3}+{x}^{2}+17{x}+38$
120000.1-h5 120000.1-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.832965173$ $0.727069403$ 5.594510179 \( \frac{35152}{9} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -108\) , \( 288\bigr] \) ${y}^2={x}^{3}+{x}^{2}-108{x}+288$
120000.1-h6 120000.1-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.665930347$ $0.363534701$ 5.594510179 \( \frac{1556068}{81} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -608\) , \( -5712\bigr] \) ${y}^2={x}^{3}+{x}^{2}-608{x}-5712$
120000.1-h7 120000.1-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.665930347$ $0.363534701$ 5.594510179 \( \frac{28756228}{3} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -1608\) , \( 24288\bigr] \) ${y}^2={x}^{3}+{x}^{2}-1608{x}+24288$
120000.1-h8 120000.1-h \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.331860695$ $0.181767350$ 5.594510179 \( \frac{3065617154}{9} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -9608\) , \( -365712\bigr] \) ${y}^2={x}^{3}+{x}^{2}-9608{x}-365712$
120000.1-i1 120000.1-i \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.209633012$ $0.531516490$ 6.175711853 \( \frac{5120}{3} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 167 a - 167\) , \( -37\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(167a-167\right){x}-37$
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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.