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Results (28 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
42588.2-a1 42588.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.324639593$ 0.490808931 \( -\frac{461661588021041}{3895443062784} a + \frac{1507573920673103}{834737799168} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 170 a + 302\) , \( -970 a + 670\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(170a+302\right){x}-970a+670$
42588.2-b1 42588.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.324639593$ 0.490808931 \( \frac{461661588021041}{3895443062784} a + \frac{19721050125360319}{11686329188352} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( -171 a + 473\) , \( 969 a - 299\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-171a+473\right){x}+969a-299$
42588.2-c1 42588.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.153886582$ $0.313083088$ 1.748165624 \( \frac{7264187703863}{7406095788} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 403\) , \( 2756\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+403{x}+2756$
42588.2-c2 42588.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.307773164$ $0.626166176$ 1.748165624 \( \frac{281397674377}{96589584} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -137\) , \( 380\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-137{x}+380$
42588.2-c3 42588.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.153886582$ $1.252332353$ 1.748165624 \( \frac{19968681097}{628992} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -57\) , \( -164\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-57{x}-164$
42588.2-c4 42588.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.615546328$ $0.313083088$ 1.748165624 \( \frac{828279937799497}{193444524} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1957\) , \( 33140\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-1957{x}+33140$
42588.2-d1 42588.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.168079577$ $0.964296414$ 2.450397098 \( -\frac{141339344329}{2167074} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -108\) , \( -486\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-108{x}-486$
42588.2-e1 42588.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.360406495$ $2.825005773$ 3.078597526 \( -\frac{47045881}{8736} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -8\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-8{x}-10$
42588.2-f1 42588.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.308022967$ $0.392808501$ 3.107185707 \( \frac{3440040594112169}{45864} a - \frac{6878875420624553}{45864} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 2496 a - 1\) , \( 15739 a + 69332\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(2496a-1\right){x}+15739a+69332$
42588.2-f2 42588.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.308022967$ $0.785617002$ 3.107185707 \( -\frac{77460685837}{460631808} a + \frac{17556307271}{230315904} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 2 a + 39\) , \( 168 a + 85\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(2a+39\right){x}+168a+85$
42588.2-f3 42588.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.654011483$ $0.785617002$ 3.107185707 \( \frac{1679410751273}{6132672} a + \frac{673156175}{876096} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 156 a - 1\) , \( 295 a + 1004\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(156a-1\right){x}+295a+1004$
42588.2-f4 42588.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.327005741$ $0.785617002$ 3.107185707 \( \frac{72992335099}{815173632} a + \frac{3644142847061}{2445520896} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 34 a - 76\) , \( 22 a + 74\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(34a-76\right){x}+22a+74$
42588.2-g1 42588.2-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.099966647$ 1.360218288 \( -\frac{1956469094246217097}{36641439744} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -26057\) , \( -1621108\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-26057{x}-1621108$
42588.2-g2 42588.2-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.299899943$ 1.360218288 \( -\frac{198461344537}{10417365504} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -122\) , \( -4948\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-122{x}-4948$
42588.2-g3 42588.2-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.899699829$ 1.360218288 \( \frac{270840023}{14329224} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 13\) , \( 182\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+13{x}+182$
42588.2-h1 42588.2-h \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.308022967$ $0.392808501$ 3.107185707 \( -\frac{3440040594112169}{45864} a - \frac{3673968831744}{49} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -2497 a + 2496\) , \( -15740 a + 85072\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2497a+2496\right){x}-15740a+85072$
42588.2-h2 42588.2-h \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.308022967$ $0.785617002$ 3.107185707 \( \frac{77460685837}{460631808} a - \frac{4705341255}{51181312} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -2 a + 41\) , \( -168 a + 253\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-2a+41\right){x}-168a+253$
42588.2-h3 42588.2-h \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.327005741$ $0.785617002$ 3.107185707 \( -\frac{72992335099}{815173632} a + \frac{148581532783}{94058496} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -34 a - 42\) , \( -22 a + 96\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-34a-42\right){x}-22a+96$
42588.2-h4 42588.2-h \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.654011483$ $0.785617002$ 3.107185707 \( -\frac{1679410751273}{6132672} a + \frac{842061422249}{3066336} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -157 a + 156\) , \( -296 a + 1300\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-157a+156\right){x}-296a+1300$
42588.2-i1 42588.2-i \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.011431035$ $0.034096494$ 11.92071101 \( -\frac{112205650221491190337}{745029571313664} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -100484\) , \( -12372091\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-100484{x}-12372091$
42588.2-j1 42588.2-j \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.019632690$ $1.501484892$ 11.23084155 \( -\frac{462900251}{326144} a - \frac{399367313}{978432} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -a - 21\) , \( -11 a + 41\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-21\right){x}-11a+41$
42588.2-k1 42588.2-k \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.019632690$ $1.501484892$ 11.23084155 \( \frac{462900251}{326144} a - \frac{894034033}{489216} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2 a - 23\) , \( 8 a + 53\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-23\right){x}+8a+53$
42588.2-l1 42588.2-l \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.780402623$ 4.719431462 \( \frac{8780064047}{32388174} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 43\) , \( 255\bigr] \) ${y}^2+{x}{y}={x}^{3}+43{x}+255$
42588.2-l2 42588.2-l \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.560805247$ 4.719431462 \( \frac{2181825073}{298116} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -27\) , \( 45\bigr] \) ${y}^2+{x}{y}={x}^{3}-27{x}+45$
42588.2-l3 42588.2-l \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $3.121610494$ 4.719431462 \( \frac{38272753}{4368} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -7\) , \( -7\bigr] \) ${y}^2+{x}{y}={x}^{3}-7{x}-7$
42588.2-l4 42588.2-l \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.780402623$ 4.719431462 \( \frac{8020417344913}{187278} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -417\) , \( 3243\bigr] \) ${y}^2+{x}{y}={x}^{3}-417{x}+3243$
42588.2-m1 42588.2-m \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.016687499$ 8.653591055 \( -\frac{5486773802537974663600129}{2635437714} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -3674496\) , \( -2711401518\bigr] \) ${y}^2+{x}{y}={x}^{3}-3674496{x}-2711401518$
42588.2-m2 42588.2-m \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/7\Z$ $\mathrm{SU}(2)$ $1$ $0.116812499$ 8.653591055 \( \frac{40251338884511}{2997011332224} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 714\) , \( -82908\bigr] \) ${y}^2+{x}{y}={x}^{3}+714{x}-82908$
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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.