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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
22400.7-a1 22400.7-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.603213731$ $0.238537141$ 2.312695188 \( \frac{185012985079}{78400000} a - \frac{650824056453}{196000000} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -592 a + 871\) , \( -2901 a - 10540\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-592a+871\right){x}-2901a-10540$
22400.7-a2 22400.7-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.206427462$ $0.238537141$ 2.312695188 \( -\frac{9103345957169}{11239424000} a - \frac{4743040859549}{5619712000} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -281 a + 823\) , \( -4977 a - 6181\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-281a+823\right){x}-4977a-6181$
22400.7-a3 22400.7-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.534404577$ $0.715611424$ 2.312695188 \( -\frac{3747996503}{9175040} a + \frac{81235193761}{45875200} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 48 a - 89\) , \( 107 a - 44\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(48a-89\right){x}+107a-44$
22400.7-a4 22400.7-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $9.619282387$ $0.079512380$ 2.312695188 \( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -11131 a - 8627\) , \( -807247 a + 7749\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-11131a-8627\right){x}-807247a+7749$
22400.7-a5 22400.7-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.068809154$ $0.715611424$ 2.312695188 \( -\frac{13113497519}{17920} a + \frac{6018146637}{17920} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 159 a + 143\) , \( 887 a - 2333\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(159a+143\right){x}+887a-2333$
22400.7-a6 22400.7-a \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.809641193$ $0.079512380$ 2.312695188 \( \frac{810722517917135481181}{23488102400} a + \frac{525145258848812643673}{11744051200} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -48092 a + 75371\) , \( -1549501 a - 7917940\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-48092a+75371\right){x}-1549501a-7917940$
22400.7-b1 22400.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.268506281$ 0.811886680 \( -\frac{92065654374401}{280} a - 328860957952 \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -5228 a - 2240\) , \( -225350 a + 75230\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5228a-2240\right){x}-225350a+75230$
22400.7-b2 22400.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.537012562$ 0.811886680 \( \frac{44957682561}{78400} a - \frac{22448742401}{39200} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -328 a - 140\) , \( -3590 a + 1310\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-328a-140\right){x}-3590a+1310$
22400.7-b3 22400.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.268506281$ 0.811886680 \( -\frac{1106567639419}{175000000} a - \frac{2848222090671}{87500000} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -651 a - 592\) , \( -11801 a - 1658\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-651a-592\right){x}-11801a-1658$
22400.7-b4 22400.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.537012562$ 0.811886680 \( -\frac{7930761861}{17920000} a + \frac{410560681}{1280000} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 19 a - 122\) , \( -529 a + 686\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(19a-122\right){x}-529a+686$
22400.7-b5 22400.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.537012562$ 0.811886680 \( \frac{9917005311763}{2936012800} a + \frac{1614739002967}{1468006400} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -135 a + 180\) , \( 251 a + 972\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-135a+180\right){x}+251a+972$
22400.7-b6 22400.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.537012562$ 0.811886680 \( \frac{1245024751}{3073280} a + \frac{717420015}{614656} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -94 a + 138\) , \( -260 a - 20\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-94a+138\right){x}-260a-20$
22400.7-c1 22400.7-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.604822983$ $1.617690403$ 2.958452916 \( -\frac{213679549}{5600} a - \frac{145076817}{5600} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -16 a - 25\) , \( -56 a - 19\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-16a-25\right){x}-56a-19$
22400.7-c2 22400.7-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.302411491$ $1.617690403$ 2.958452916 \( -\frac{797873}{5120} a + \frac{1748809}{7168} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -8 a - 1\) , \( -11 a - 20\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-8a-1\right){x}-11a-20$
22400.7-d1 22400.7-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.383560264$ $1.428132098$ 3.312630161 \( -\frac{2539645}{3136} a + \frac{256038103}{78400} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 16 a + 7\) , \( 8 a - 51\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(16a+7\right){x}+8a-51$
22400.7-d2 22400.7-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.767120528$ $1.428132098$ 3.312630161 \( \frac{160514353}{13720} a + \frac{206785941}{13720} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -9 a + 43\) , \( 95 a - 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9a+43\right){x}+95a-5$
22400.7-e1 22400.7-e \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.257479238$ $2.326904652$ 3.623195484 \( \frac{1457}{140} a - \frac{6159}{700} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 0\) , \( 4 a - 12\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+4a-12$
22400.7-e2 22400.7-e \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.514958476$ $2.326904652$ 3.623195484 \( \frac{1889729}{70} a + \frac{191899}{10} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -8 a - 12\) , \( -20 a - 8\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-8a-12\right){x}-20a-8$
22400.7-f1 22400.7-f \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.132856079$ 1.712717404 \( -\frac{82248083}{179200} a + \frac{347879361}{179200} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -6 a - 34\) , \( 4 a - 48\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-6a-34\right){x}+4a-48$
22400.7-f2 22400.7-f \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.132856079$ 1.712717404 \( \frac{105641161}{2240} a + \frac{136495}{28} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 49 a - 68\) , \( 201 a - 112\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(49a-68\right){x}+201a-112$
22400.7-g1 22400.7-g \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.421990124$ $2.502092659$ 3.192615688 \( \frac{103823}{70} a + \frac{103823}{350} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -3 a + 5\) , \( -3 a + 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a+5\right){x}-3a+1$
22400.7-g2 22400.7-g \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.210995062$ $2.502092659$ 3.192615688 \( -\frac{154207}{140} a + \frac{171741}{140} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -9\) , \( -a - 8\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-9{x}-a-8$
22400.7-h1 22400.7-h \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.042234365$ $0.268506281$ 3.316125759 \( \frac{92065654374401}{280} a - \frac{184146722600961}{280} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 1492 a + 7467\) , \( 211017 a - 209936\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(1492a+7467\right){x}+211017a-209936$
22400.7-h2 22400.7-h \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.084468731$ $0.268506281$ 3.316125759 \( \frac{1106567639419}{175000000} a - \frac{6803011820761}{175000000} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 405 a + 933\) , \( 10708 a - 16352\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(405a+933\right){x}+10708a-16352$
22400.7-h3 22400.7-h \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.042234365$ $0.537012562$ 3.316125759 \( \frac{7930761861}{17920000} a - \frac{2182912327}{17920000} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 85 a - 27\) , \( 596 a - 96\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(85a-27\right){x}+596a-96$
22400.7-h4 22400.7-h \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.021117182$ $0.537012562$ 3.316125759 \( -\frac{44957682561}{78400} a + \frac{60197759}{78400} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 92 a + 467\) , \( 3257 a - 3296\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(92a+467\right){x}+3257a-3296$
22400.7-h5 22400.7-h \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.510558591$ $0.537012562$ 3.316125759 \( -\frac{1245024751}{3073280} a + \frac{2416062413}{1536640} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -100 a + 131\) , \( 328 a - 467\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-100a+131\right){x}+328a-467$
22400.7-h6 22400.7-h \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.021117182$ $0.537012562$ 3.316125759 \( -\frac{9917005311763}{2936012800} a + \frac{13146483317697}{2936012800} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -129 a + 187\) , \( 87 a + 1171\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-129a+187\right){x}+87a+1171$
22400.7-i1 22400.7-i \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.346848112$ $1.702706066$ 3.571494468 \( \frac{13179}{19600} a + \frac{89927}{19600} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a\) , \( -3 a + 28\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-3a{x}-3a+28$
22400.7-i2 22400.7-i \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.693696225$ $1.702706066$ 3.571494468 \( -\frac{6821623}{8960} a + \frac{55209257}{1792} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 14 a - 30\) , \( -48 a + 44\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(14a-30\right){x}-48a+44$
22400.7-i3 22400.7-i \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.693696225$ $1.702706066$ 3.571494468 \( \frac{477521691}{17500} a + \frac{802743911}{17500} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 26 a - 18\) , \( 42 a + 12\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(26a-18\right){x}+42a+12$
22400.7-i4 22400.7-i \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.173424056$ $0.851353033$ 3.571494468 \( -\frac{1321487249}{48020} a + \frac{754040943}{9604} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -103 a + 100\) , \( -123 a + 668\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-103a+100\right){x}-123a+668$
22400.7-j1 22400.7-j \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.308129490$ 1.977705894 \( \frac{385902711}{8960} a - \frac{838409589}{4480} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -8 a - 65\) , \( -62 a - 211\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-8a-65\right){x}-62a-211$
22400.7-j2 22400.7-j \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.308129490$ 1.977705894 \( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 46 a + 13\) , \( 22 a + 209\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(46a+13\right){x}+22a+209$
22400.7-j3 22400.7-j \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.308129490$ 1.977705894 \( \frac{1367631}{2800} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -11 a + 16\) , \( 35 a - 14\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-11a+16\right){x}+35a-14$
22400.7-j4 22400.7-j \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.654064745$ 1.977705894 \( \frac{611960049}{122500} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 89 a - 124\) , \( 407 a - 330\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(89a-124\right){x}+407a-330$
22400.7-j5 22400.7-j \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.327032372$ 1.977705894 \( \frac{74565301329}{5468750} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 439 a - 614\) , \( -4955 a + 2876\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(439a-614\right){x}-4955a+2876$
22400.7-j6 22400.7-j \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.327032372$ 1.977705894 \( \frac{2121328796049}{120050} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 1339 a - 1874\) , \( 28857 a - 19680\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(1339a-1874\right){x}+28857a-19680$
22400.7-k1 22400.7-k \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.203840522$ $1.421498015$ 6.133039862 \( -\frac{15989226301}{22400} a - \frac{6703640913}{22400} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -9 a + 83\) , \( 193 a - 31\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a+83\right){x}+193a-31$
22400.7-k2 22400.7-k \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.101920261$ $1.421498015$ 6.133039862 \( \frac{348212521}{573440} a - \frac{17351351}{114688} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 11 a + 3\) , \( 15 a + 23\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11a+3\right){x}+15a+23$
22400.7-l1 22400.7-l \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.715611424$ 3.245708337 \( \frac{13113497519}{17920} a - \frac{3547675441}{8960} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -99 a - 227\) , \( 747 a + 1187\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-99a-227\right){x}+747a+1187$
22400.7-l2 22400.7-l \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.238537141$ 3.245708337 \( \frac{9103345957169}{11239424000} a - \frac{2655632525181}{1605632000} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -584 a + 388\) , \( -3807 a + 13169\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-584a+388\right){x}-3807a+13169$
22400.7-l3 22400.7-l \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.238537141$ 3.245708337 \( -\frac{185012985079}{78400000} a - \frac{376583187511}{392000000} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -624 a + 828\) , \( -685 a + 13323\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-624a+828\right){x}-685a+13323$
22400.7-l4 22400.7-l \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.715611424$ 3.245708337 \( \frac{3747996503}{9175040} a + \frac{31247605623}{22937600} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 61 a - 67\) , \( 93 a - 131\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(61a-67\right){x}+93a-131$
22400.7-l5 22400.7-l \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.079512380$ 3.245708337 \( -\frac{41282203518025836237719}{630503947831869440} a + \frac{37460205421439226610825}{126100789566373888} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 5891 a + 15963\) , \( -693027 a + 970909\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5891a+15963\right){x}-693027a+970909$
22400.7-l6 22400.7-l \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.079512380$ 3.245708337 \( -\frac{810722517917135481181}{23488102400} a + \frac{1861013035614760768527}{23488102400} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -53749 a + 67203\) , \( -56785 a + 8996823\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-53749a+67203\right){x}-56785a+8996823$
22400.7-m1 22400.7-m \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.192170278$ $1.014067406$ 5.892424295 \( \frac{741041193}{36700160} a + \frac{196817993}{7340032} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5 a - 10\) , \( -85 a + 94\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-5a-10\right){x}-85a+94$
22400.7-m2 22400.7-m \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.192170278$ $1.014067406$ 5.892424295 \( \frac{68488403}{140000} a + \frac{540576223}{140000} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -25 a - 37\) , \( -101 a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a-37\right){x}-101a+3$
22400.7-m3 22400.7-m \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.384340557$ $1.014067406$ 5.892424295 \( -\frac{523907907}{179200} a + \frac{3285243089}{179200} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -56 a + 55\) , \( -24 a + 265\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-56a+55\right){x}-24a+265$
22400.7-m4 22400.7-m \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.768681115$ $0.507033703$ 5.892424295 \( -\frac{739298508457}{7840} a + \frac{457662685527}{1568} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -856 a + 855\) , \( -2584 a + 17225\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-856a+855\right){x}-2584a+17225$
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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.