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Results (32 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
28672.9-a1 28672.9-a \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.998327441$ $1.394083610$ 4.208262259 \( -\frac{1143001}{28} a - \frac{3214301}{28} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 12 a - 64\) , \( -76 a + 204\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(12a-64\right){x}-76a+204$
28672.9-a2 28672.9-a \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $2.495818603$ $0.557633444$ 4.208262259 \( \frac{581506766557}{359661568} a + \frac{72912600945}{359661568} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 82 a + 76\) , \( 64 a - 860\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(82a+76\right){x}+64a-860$
28672.9-a3 28672.9-a \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.499163720$ $2.788167220$ 4.208262259 \( -\frac{5363}{112} a + \frac{52833}{112} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 4\) , \( 4\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-4\right){x}+4$
28672.9-a4 28672.9-a \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $4.991637207$ $0.278816722$ 4.208262259 \( -\frac{243980943049}{17210368} a + \frac{37738852723}{17210368} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 92 a + 976\) , \( -9324 a + 6188\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(92a+976\right){x}-9324a+6188$
28672.9-b1 28672.9-b \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.733894296$ 2.066629834 \( \frac{225856}{7} a - \frac{120192}{7} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3 a - 11\) , \( 2 a + 18\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-11\right){x}+2a+18$
28672.9-b2 28672.9-b \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.733894296$ 2.066629834 \( \frac{3728}{49} a - \frac{2672}{49} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -3\) , \( 3 a + 2\bigr] \) ${y}^2={x}^{3}+a{x}^{2}-3{x}+3a+2$
28672.9-c1 28672.9-c \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.949735186$ $3.128064916$ 4.491477793 \( -\frac{1072}{7} a + \frac{3280}{7} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 1\) , \( -3 a + 2\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-2a+1\right){x}-3a+2$
28672.9-c2 28672.9-c \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.474867593$ $3.128064916$ 4.491477793 \( \frac{9244}{7} a + \frac{31692}{7} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a + 4\) , \( -4 a + 8\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+4\right){x}-4a+8$
28672.9-d1 28672.9-d \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.562354823$ 2.362058470 \( \frac{608715}{49} a - \frac{161001}{49} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 23 a - 21\) , \( -50 a + 6\bigr] \) ${y}^2={x}^{3}+\left(23a-21\right){x}-50a+6$
28672.9-d2 28672.9-d \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.562354823$ 2.362058470 \( -\frac{12393}{343} a - \frac{52461}{343} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 5 a - 9\) , \( -26 a + 22\bigr] \) ${y}^2={x}^{3}+\left(5a-9\right){x}-26a+22$
28672.9-e1 28672.9-e \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.067882687$ 1.614486868 \( -\frac{23725299}{896} a - \frac{4281957791}{896} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -120 a + 121\) , \( 149 a - 990\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-120a+121\right){x}+149a-990$
28672.9-e2 28672.9-e \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.067882687$ 1.614486868 \( \frac{182016677}{114688} a - \frac{7149735}{114688} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a + 40\) , \( 56 a - 80\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a+40\right){x}+56a-80$
28672.9-f1 28672.9-f \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.290751244$ $2.736244025$ 4.811133086 \( \frac{11418}{7} a - \frac{127870}{7} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 7\) , \( -9 a - 6\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(8a-7\right){x}-9a-6$
28672.9-f2 28672.9-f \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.581502488$ $2.736244025$ 4.811133086 \( \frac{4532}{7} a - \frac{5052}{7} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a\) , \( 4 a - 4\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}-4a{x}+4a-4$
28672.9-g1 28672.9-g \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $1.648402668$ $1.031781713$ 5.142710798 \( \frac{31083}{98} a - \frac{338111}{686} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 20 a - 24\) , \( 84 a - 84\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(20a-24\right){x}+84a-84$
28672.9-g2 28672.9-g \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.824201334$ $2.063563427$ 5.142710798 \( -\frac{1104701}{196} a + \frac{620975}{196} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -10 a - 4\) , \( 16 a + 4\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-4\right){x}+16a+4$
28672.9-h1 28672.9-h \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.736289018$ $1.934816705$ 4.307538015 \( \frac{11418}{7} a - \frac{127870}{7} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -9 a + 22\) , \( -21 a - 14\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-9a+22\right){x}-21a-14$
28672.9-h2 28672.9-h \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.368144509$ $3.869633410$ 4.307538015 \( \frac{4532}{7} a - \frac{5052}{7} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( a + 2\) , \( a - 2\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(a+2\right){x}+a-2$
28672.9-i1 28672.9-i \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.184934948$ $1.459159692$ 4.895691373 \( \frac{31083}{98} a - \frac{338111}{686} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -11 a + 2\) , \( 21 a - 42\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-11a+2\right){x}+21a-42$
28672.9-i2 28672.9-i \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.369869896$ $1.459159692$ 4.895691373 \( -\frac{1104701}{196} a + \frac{620975}{196} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 24 a - 16\) , \( 28 a + 44\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(24a-16\right){x}+28a+44$
28672.9-j1 28672.9-j \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.755107089$ 2.283229226 \( -\frac{23725299}{896} a - \frac{4281957791}{896} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 119 a - 362\) , \( 1169 a - 2310\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(119a-362\right){x}+1169a-2310$
28672.9-j2 28672.9-j \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.510214179$ 2.283229226 \( \frac{182016677}{114688} a - \frac{7149735}{114688} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 9 a - 22\) , \( 11 a - 34\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(9a-22\right){x}+11a-34$
28672.9-k1 28672.9-k \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.240387146$ $2.209503381$ 4.818014847 \( \frac{608715}{49} a - \frac{161001}{49} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -11 a - 1\) , \( -18 a + 14\bigr] \) ${y}^2={x}^{3}+\left(-11a-1\right){x}-18a+14$
28672.9-k2 28672.9-k \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.480774292$ $1.104751690$ 4.818014847 \( -\frac{12393}{343} a - \frac{52461}{343} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 19\) , \( -74 a + 14\bigr] \) ${y}^2={x}^{3}+\left(-a+19\right){x}-74a+14$
28672.9-l1 28672.9-l \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.971531948$ 2.980676135 \( -\frac{1143001}{28} a - \frac{3214301}{28} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -19 a + 26\) , \( -3 a + 70\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-19a+26\right){x}-3a+70$
28672.9-l2 28672.9-l \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.394306389$ 2.980676135 \( \frac{581506766557}{359661568} a + \frac{72912600945}{359661568} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -240 a + 88\) , \( 988 a - 2452\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-240a+88\right){x}+988a-2452$
28672.9-l3 28672.9-l \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.971531948$ 2.980676135 \( -\frac{5363}{112} a + \frac{52833}{112} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8\) , \( -4 a + 12\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+8{x}-4a+12$
28672.9-l4 28672.9-l \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.394306389$ 2.980676135 \( -\frac{243980943049}{17210368} a + \frac{37738852723}{17210368} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 221 a - 534\) , \( -2723 a + 3878\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(221a-534\right){x}-2723a+3878$
28672.9-m1 28672.9-m \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $3.866310392$ 2.922655939 \( \frac{225856}{7} a - \frac{120192}{7} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a + 7\) , \( 3 a + 4\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-2a+7\right){x}+3a+4$
28672.9-m2 28672.9-m \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.933155196$ 2.922655939 \( \frac{3728}{49} a - \frac{2672}{49} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 3 a + 2\) , \( 7 a + 14\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(3a+2\right){x}+7a+14$
28672.9-n1 28672.9-n \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $4.423751828$ 3.344042057 \( -\frac{1072}{7} a + \frac{3280}{7} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+2a{x}$
28672.9-n2 28672.9-n \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.211875914$ 3.344042057 \( \frac{9244}{7} a + \frac{31692}{7} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -8 a\) , \( -16 a + 16\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}-8a{x}-16a+16$
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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.