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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
19.1-a1 19.1-a \(\Q(\sqrt{-19}) \) \( 19 \) $0$ $\mathsf{trivial}$ $1$ $0.935309008$ 0.858298410 \( -\frac{50357871050752}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) ${y}^2+{y}={x}^3+{x}^2-769{x}-8470$
19.1-a2 19.1-a \(\Q(\sqrt{-19}) \) \( 19 \) $0$ $\Z/3\Z$ $1$ $2.805927025$ 0.858298410 \( -\frac{89915392}{6859} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) ${y}^2+{y}={x}^3+{x}^2-9{x}-15$
19.1-a3 19.1-a \(\Q(\sqrt{-19}) \) \( 19 \) $0$ $\Z/3\Z$ $1$ $8.417781075$ 0.858298410 \( \frac{32768}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^3+{x}^2+{x}$
20.1-a1 20.1-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5 \) $0$ $\mathsf{trivial}$ $1$ $1.041796112$ 0.956017679 \( \frac{546495468563548}{3814697265625} a - \frac{26594457793024591}{7629394531250} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -15 a - 31\) , \( -54 a - 60\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-15a-31\right){x}-54a-60$
20.1-a2 20.1-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/3\Z$ $1$ $9.376165015$ 0.956017679 \( -\frac{16129}{50} a + \frac{10942}{25} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2-{x}$
20.1-a3 20.1-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/3\Z$ $1$ $3.125388338$ 0.956017679 \( -\frac{1697253523}{15625} a + \frac{9034902289}{125000} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a + 9\) , \( -2 a - 24\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-5a+9\right){x}-2a-24$
20.2-a1 20.2-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/3\Z$ $1$ $3.125388338$ 0.956017679 \( \frac{1697253523}{15625} a - \frac{908625179}{25000} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( 2 a - 26\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(4a+4\right){x}+2a-26$
20.2-a2 20.2-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5 \) $0$ $\mathsf{trivial}$ $1$ $1.041796112$ 0.956017679 \( -\frac{546495468563548}{3814697265625} a - \frac{5100293371179499}{1525878906250} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 14 a - 46\) , \( 54 a - 114\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(14a-46\right){x}+54a-114$
20.2-a3 20.2-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/3\Z$ $1$ $9.376165015$ 0.956017679 \( \frac{16129}{50} a + \frac{1151}{10} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}$
44.1-a1 44.1-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $0.157781648$ $4.016441512$ 1.163084113 \( -\frac{1436117}{15488} a + \frac{10855315}{3872} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( a - 1\) , \( -a\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}-a$
44.2-a1 44.2-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $0.157781648$ $4.016441512$ 1.163084113 \( \frac{1436117}{15488} a + \frac{41985143}{15488} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -2 a + 1\) , \( 0\bigr] \) ${y}^2+{x}{y}+a{y}={x}^3+\left(-2a+1\right){x}$
49.3-CMa1 49.3-CMa \(\Q(\sqrt{-19}) \) \( 7^{2} \) $0$ $\mathsf{trivial}$ $-19$ $1$ $3.318662149$ 1.522706625 \( -884736 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -6 a - 2\) , \( -9 a + 9\bigr] \) ${y}^2+{y}={x}^3+\left(-6a-2\right){x}-9a+9$
76.1-a1 76.1-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $0.965055962$ 0.885596087 \( -\frac{37966934881}{4952198} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -279\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-70{x}-279$
76.1-a2 76.1-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 19 \) $0$ $\Z/5\Z$ $1$ $4.825279813$ 0.885596087 \( -\frac{1}{608} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2+1$
76.1-b1 76.1-b \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 19 \) $1$ $\Z/3\Z$ $0.774675563$ $3.410590199$ 1.616372036 \( -\frac{413493625}{152} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -16\) , \( 22\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-16{x}+22$
76.1-b2 76.1-b \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $0.086075062$ $0.378954466$ 1.616372036 \( -\frac{69173457625}{2550136832} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -86\) , \( -2456\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-86{x}-2456$
76.1-b3 76.1-b \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 19 \) $1$ $\Z/3\Z$ $0.258225187$ $1.136863399$ 1.616372036 \( \frac{94196375}{3511808} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 9\) , \( 90\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+9{x}+90$
85.2-a1 85.2-a \(\Q(\sqrt{-19}) \) \( 5 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $4.115004555$ 1.888093579 \( \frac{3619812216}{180625} a - \frac{3820287361}{180625} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 4\) , \( -4 a + 1\bigr] \) ${y}^2+{x}{y}={x}^3-a{x}^2+4{x}-4a+1$
85.2-a2 85.2-a \(\Q(\sqrt{-19}) \) \( 5 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $8.230009110$ 1.888093579 \( -\frac{205232}{425} a + \frac{620697}{425} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^3-a{x}^2-{x}$
85.3-a1 85.3-a \(\Q(\sqrt{-19}) \) \( 5 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $4.115004555$ 1.888093579 \( -\frac{3619812216}{180625} a - \frac{40095029}{36125} \) \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 4\) , \( 4 a - 3\bigr] \) ${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+4{x}+4a-3$
85.3-a2 85.3-a \(\Q(\sqrt{-19}) \) \( 5 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $8.230009110$ 1.888093579 \( \frac{205232}{425} a + \frac{83093}{85} \) \( \bigl[1\) , \( a - 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2-{x}$
100.1-a1 100.1-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $1.941303345$ $0.465905385$ 1.659985596 \( \frac{546495468563548}{3814697265625} a - \frac{26594457793024591}{7629394531250} \) \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 29 a + 223\) , \( -697 a + 1006\bigr] \) ${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(29a+223\right){x}-697a+1006$
100.1-a2 100.1-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.215700371$ $4.193148468$ 1.659985596 \( -\frac{16129}{50} a + \frac{10942}{25} \) \( \bigl[1\) , \( a - 1\) , \( 0\) , \( -a - 2\) , \( -a + 1\bigr] \) ${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(-a-2\right){x}-a+1$
100.1-a3 100.1-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.647101115$ $1.397716156$ 1.659985596 \( -\frac{1697253523}{15625} a + \frac{9034902289}{125000} \) \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 29 a - 27\) , \( -85 a - 104\bigr] \) ${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(29a-27\right){x}-85a-104$
100.3-a1 100.3-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.647101115$ $1.397716156$ 1.659985596 \( \frac{1697253523}{15625} a - \frac{908625179}{25000} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( -29 a + 2\) , \( 85 a - 189\bigr] \) ${y}^2+{x}{y}={x}^3-a{x}^2+\left(-29a+2\right){x}+85a-189$
100.3-a2 100.3-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $1.941303345$ $0.465905385$ 1.659985596 \( -\frac{546495468563548}{3814697265625} a - \frac{5100293371179499}{1525878906250} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( -29 a + 252\) , \( 697 a + 309\bigr] \) ${y}^2+{x}{y}={x}^3-a{x}^2+\left(-29a+252\right){x}+697a+309$
100.3-a3 100.3-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.215700371$ $4.193148468$ 1.659985596 \( \frac{16129}{50} a + \frac{1151}{10} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( a - 3\) , \( a\bigr] \) ${y}^2+{x}{y}={x}^3-a{x}^2+\left(a-3\right){x}+a$
121.2-a1 121.2-a \(\Q(\sqrt{-19}) \) \( 11^{2} \) $1$ $\mathsf{trivial}$ $5.612837583$ $0.370308724$ 1.907346561 \( -\frac{52893159101157376}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) ${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$
121.2-a2 121.2-a \(\Q(\sqrt{-19}) \) \( 11^{2} \) $1$ $\Z/5\Z$ $1.122567516$ $1.851543623$ 1.907346561 \( -\frac{122023936}{161051} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) ${y}^2+{y}={x}^3-{x}^2-10{x}-20$
121.2-a3 121.2-a \(\Q(\sqrt{-19}) \) \( 11^{2} \) $1$ $\Z/5\Z$ $5.612837583$ $9.257718117$ 1.907346561 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3-{x}^2$
171.1-a1 171.1-a \(\Q(\sqrt{-19}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/2\Z$ $1$ $1.632344499$ 0.374485511 \( \frac{67419143}{390963} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+8{x}+29$
171.1-a2 171.1-a \(\Q(\sqrt{-19}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/4\Z$ $1$ $6.529377996$ 0.374485511 \( \frac{389017}{57} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-2{x}-1$
171.1-a3 171.1-a \(\Q(\sqrt{-19}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.264688998$ 0.374485511 \( \frac{30664297}{3249} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-7{x}+5$
171.1-a4 171.1-a \(\Q(\sqrt{-19}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/4\Z$ $1$ $1.632344499$ 0.374485511 \( \frac{115714886617}{1539} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-102{x}+385$
171.1-b1 171.1-b \(\Q(\sqrt{-19}) \) \( 3^{2} \cdot 19 \) $2$ $\mathsf{trivial}$ $0.044869955$ $5.328644115$ 1.755276488 \( -\frac{1404928}{171} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -2\) , \( 2\bigr] \) ${y}^2+{y}={x}^3-{x}^2-2{x}+2$
171.1-c1 171.1-c \(\Q(\sqrt{-19}) \) \( 3^{2} \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $0.271765830$ 1.995115434 \( -\frac{9358714467168256}{22284891} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -4390\) , \( -113432\bigr] \) ${y}^2+{y}={x}^3+{x}^2-4390{x}-113432$
171.1-c2 171.1-c \(\Q(\sqrt{-19}) \) \( 3^{2} \cdot 19 \) $0$ $\Z/5\Z$ $1$ $1.358829150$ 1.995115434 \( \frac{841232384}{1121931} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 20\) , \( -32\bigr] \) ${y}^2+{y}={x}^3+{x}^2+20{x}-32$
175.2-a1 175.2-a \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $1$ $\mathsf{trivial}$ $0.062767475$ $5.334923105$ 1.843729767 \( -\frac{654642}{343} a + \frac{1310769}{343} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+{x}^2$
175.2-b1 175.2-b \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $2.385850143$ 2.189406246 \( -\frac{654642}{343} a + \frac{1310769}{343} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -4 a + 7\) , \( 7 a - 18\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-4a+7\right){x}+7a-18$
175.3-a1 175.3-a \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.757058949$ 1.723856872 \( \frac{21610347}{12005} a - \frac{741467764}{60025} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -a - 2\) , \( -a - 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-2\right){x}-a-1$
175.3-a2 175.3-a \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $7.514117899$ 1.723856872 \( \frac{72237}{245} a - \frac{228761}{245} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -a + 3\) , \( 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+3\right){x}+1$
175.3-a3 175.3-a \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $0$ $\Z/4\Z$ $1$ $1.878529474$ 1.723856872 \( -\frac{2532825772081}{3603000625} a - \frac{1341942703599}{3603000625} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 4 a - 7\) , \( -13 a + 6\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(4a-7\right){x}-13a+6$
175.3-a4 175.3-a \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.878529474$ 1.723856872 \( -\frac{1344745702751}{30625} a + \frac{948946059331}{6125} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -6 a - 77\) , \( -33 a - 236\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-6a-77\right){x}-33a-236$
175.4-a1 175.4-a \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $3.757058949$ 1.723856872 \( -\frac{21610347}{12005} a - \frac{633416029}{60025} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a - 3\) , \( -2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-a-3\right){x}-2$
175.4-a2 175.4-a \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $0$ $\Z/4\Z$ $1$ $1.878529474$ 1.723856872 \( \frac{2532825772081}{3603000625} a - \frac{774953695136}{720600125} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -6 a - 3\) , \( 12 a - 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-6a-3\right){x}+12a-7$
175.4-a3 175.4-a \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $7.514117899$ 1.723856872 \( -\frac{72237}{245} a - \frac{156524}{245} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a + 2\) , \( -a + 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-a+2\right){x}-a+1$
175.4-a4 175.4-a \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.878529474$ 1.723856872 \( \frac{1344745702751}{30625} a + \frac{3399984593904}{30625} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 4 a - 83\) , \( 32 a - 269\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(4a-83\right){x}+32a-269$
175.5-a1 175.5-a \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $1$ $\mathsf{trivial}$ $0.062767475$ $5.334923105$ 1.843729767 \( \frac{654642}{343} a + \frac{656127}{343} \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2$
175.5-b1 175.5-b \(\Q(\sqrt{-19}) \) \( 5^{2} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $2.385850143$ 2.189406246 \( \frac{654642}{343} a + \frac{656127}{343} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 5 a - 2\) , \( -3 a - 13\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(5a-2\right){x}-3a-13$
196.1-a1 196.1-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $3.751213062$ 1.721174595 \( -\frac{27}{8} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( a + 3\) , \( -2 a + 2\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(a+3\right){x}-2a+2$
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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.