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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
28672.5-a1 28672.5-a \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.998327441$ $1.394083610$ 4.208262259 \( \frac{1143001}{28} a - \frac{2178651}{14} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -12 a - 52\) , \( 76 a + 128\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-12a-52\right){x}+76a+128$
28672.5-a2 28672.5-a \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $4.991637207$ $0.278816722$ 4.208262259 \( \frac{243980943049}{17210368} a - \frac{103121045163}{8605184} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -92 a + 1068\) , \( 9324 a - 3136\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-92a+1068\right){x}+9324a-3136$
28672.5-a3 28672.5-a \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.499163720$ $2.788167220$ 4.208262259 \( \frac{5363}{112} a + \frac{23735}{56} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a - 2\) , \( 4\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-2a-2\right){x}+4$
28672.5-a4 28672.5-a \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $2.495818603$ $0.557633444$ 4.208262259 \( -\frac{581506766557}{359661568} a + \frac{327209683751}{179830784} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -82 a + 158\) , \( -64 a - 796\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-82a+158\right){x}-64a-796$
28672.5-b1 28672.5-b \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.733894296$ 2.066629834 \( -\frac{3728}{49} a + \frac{1056}{49} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3\) , \( -3 a + 5\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-3{x}-3a+5$
28672.5-b2 28672.5-b \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.733894296$ 2.066629834 \( -\frac{225856}{7} a + \frac{105664}{7} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a - 14\) , \( -2 a + 20\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(3a-14\right){x}-2a+20$
28672.5-c1 28672.5-c \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.949735186$ $3.128064916$ 4.491477793 \( \frac{1072}{7} a + \frac{2208}{7} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 1\) , \( 3 a - 1\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-1\right){x}+3a-1$
28672.5-c2 28672.5-c \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.474867593$ $3.128064916$ 4.491477793 \( -\frac{9244}{7} a + 5848 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 6\) , \( 4 a + 4\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-2a+6\right){x}+4a+4$
28672.5-d1 28672.5-d \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.562354823$ 2.362058470 \( \frac{12393}{343} a - \frac{64854}{343} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -5 a - 4\) , \( 26 a - 4\bigr] \) ${y}^2={x}^{3}+\left(-5a-4\right){x}+26a-4$
28672.5-d2 28672.5-d \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.562354823$ 2.362058470 \( -\frac{608715}{49} a + \frac{447714}{49} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -23 a + 2\) , \( 50 a - 44\bigr] \) ${y}^2={x}^{3}+\left(-23a+2\right){x}+50a-44$
28672.5-e1 28672.5-e \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.067882687$ 1.614486868 \( \frac{23725299}{896} a - \frac{2152841545}{448} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 120 a + 1\) , \( -149 a - 841\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(120a+1\right){x}-149a-841$
28672.5-e2 28672.5-e \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.067882687$ 1.614486868 \( -\frac{182016677}{114688} a + \frac{87433471}{57344} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -4 a + 44\) , \( -56 a - 24\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-4a+44\right){x}-56a-24$
28672.5-f1 28672.5-f \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.290751244$ $2.736244025$ 4.811133086 \( -\frac{11418}{7} a - 16636 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8 a + 1\) , \( 9 a - 15\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+1\right){x}+9a-15$
28672.5-f2 28672.5-f \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.581502488$ $2.736244025$ 4.811133086 \( -\frac{4532}{7} a - \frac{520}{7} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 4\) , \( -4 a\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(4a-4\right){x}-4a$
28672.5-g1 28672.5-g \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.824201334$ $2.063563427$ 5.142710798 \( \frac{1104701}{196} a - \frac{241863}{98} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 14\) , \( -16 a + 20\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(10a-14\right){x}-16a+20$
28672.5-g2 28672.5-g \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $1.648402668$ $1.031781713$ 5.142710798 \( -\frac{31083}{98} a - \frac{60265}{343} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a - 4\) , \( -84 a\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-20a-4\right){x}-84a$
28672.5-h1 28672.5-h \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.736289018$ $1.934816705$ 4.307538015 \( -\frac{11418}{7} a - 16636 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 9 a + 13\) , \( 21 a - 35\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(9a+13\right){x}+21a-35$
28672.5-h2 28672.5-h \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.368144509$ $3.869633410$ 4.307538015 \( -\frac{4532}{7} a - \frac{520}{7} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -a + 3\) , \( -a - 1\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-a+3\right){x}-a-1$
28672.5-i1 28672.5-i \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.755107089$ 2.283229226 \( \frac{23725299}{896} a - \frac{2152841545}{448} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -119 a - 243\) , \( -1169 a - 1141\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-119a-243\right){x}-1169a-1141$
28672.5-i2 28672.5-i \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.510214179$ 2.283229226 \( -\frac{182016677}{114688} a + \frac{87433471}{57344} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -9 a - 13\) , \( -11 a - 23\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-9a-13\right){x}-11a-23$
28672.5-j1 28672.5-j \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.369869896$ $1.459159692$ 4.895691373 \( \frac{1104701}{196} a - \frac{241863}{98} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -22 a + 7\) , \( -51 a + 79\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-22a+7\right){x}-51a+79$
28672.5-j2 28672.5-j \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.184934948$ $1.459159692$ 4.895691373 \( -\frac{31083}{98} a - \frac{60265}{343} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 11 a - 9\) , \( -21 a - 21\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(11a-9\right){x}-21a-21$
28672.5-k1 28672.5-k \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.480774292$ $1.104751690$ 4.818014847 \( \frac{12393}{343} a - \frac{64854}{343} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( a + 18\) , \( 74 a - 60\bigr] \) ${y}^2={x}^{3}+\left(a+18\right){x}+74a-60$
28672.5-k2 28672.5-k \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.240387146$ $2.209503381$ 4.818014847 \( -\frac{608715}{49} a + \frac{447714}{49} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 11 a - 12\) , \( 18 a - 4\bigr] \) ${y}^2={x}^{3}+\left(11a-12\right){x}+18a-4$
28672.5-l1 28672.5-l \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.971531948$ 2.980676135 \( \frac{1143001}{28} a - \frac{2178651}{14} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 19 a + 7\) , \( 3 a + 67\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(19a+7\right){x}+3a+67$
28672.5-l2 28672.5-l \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.394306389$ 2.980676135 \( \frac{243980943049}{17210368} a - \frac{103121045163}{8605184} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -221 a - 313\) , \( 2723 a + 1155\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-221a-313\right){x}+2723a+1155$
28672.5-l3 28672.5-l \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.971531948$ 2.980676135 \( \frac{5363}{112} a + \frac{23735}{56} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 7\) , \( 5 a + 15\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+7\right){x}+5a+15$
28672.5-l4 28672.5-l \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.394306389$ 2.980676135 \( -\frac{581506766557}{359661568} a + \frac{327209683751}{179830784} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 242 a - 153\) , \( -747 a - 1617\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(242a-153\right){x}-747a-1617$
28672.5-m1 28672.5-m \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.933155196$ 2.922655939 \( -\frac{3728}{49} a + \frac{1056}{49} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -3 a + 5\) , \( -7 a + 21\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-3a+5\right){x}-7a+21$
28672.5-m2 28672.5-m \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $3.866310392$ 2.922655939 \( -\frac{225856}{7} a + \frac{105664}{7} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a + 5\) , \( -3 a + 7\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(2a+5\right){x}-3a+7$
28672.5-n1 28672.5-n \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $4.423751828$ 3.344042057 \( \frac{1072}{7} a + \frac{2208}{7} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1\) , \( a - 1\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+{x}+a-1$
28672.5-n2 28672.5-n \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.211875914$ 3.344042057 \( -\frac{9244}{7} a + 5848 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 9\) , \( 7 a + 9\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-9\right){x}+7a+9$
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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.