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Results (8 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
18.1-a1 18.1-a \(\Q(\sqrt{19}) \) \( 2 \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.365735541$ 2.154222274 \( -\frac{81634634531}{22674816} a + \frac{204402908939}{11337408} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -6112 a - 26627\) , \( -275601 a - 1201300\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6112a-26627\right){x}-275601a-1201300$
18.1-a2 18.1-a \(\Q(\sqrt{19}) \) \( 2 \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.682867770$ 2.154222274 \( \frac{3015980695953593}{502096953744} a + \frac{13147717480342991}{502096953744} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -46792 a - 203947\) , \( 11319975 a + 49342644\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-46792a-203947\right){x}+11319975a+49342644$
18.1-b1 18.1-b \(\Q(\sqrt{19}) \) \( 2 \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.682867770$ 2.154222274 \( -\frac{3015980695953593}{502096953744} a + \frac{13147717480342991}{502096953744} \) \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 46791 a - 203947\) , \( -11319976 a + 49342644\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(46791a-203947\right){x}-11319976a+49342644$
18.1-b2 18.1-b \(\Q(\sqrt{19}) \) \( 2 \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.365735541$ 2.154222274 \( \frac{81634634531}{22674816} a + \frac{204402908939}{11337408} \) \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 6111 a - 26627\) , \( 275600 a - 1201300\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6111a-26627\right){x}+275600a-1201300$
18.1-c1 18.1-c \(\Q(\sqrt{19}) \) \( 2 \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.134555585$ $10.28817665$ 1.746731012 \( -\frac{81634634531}{22674816} a + \frac{204402908939}{11337408} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( -6110 a - 26622\) , \( 269490 a + 1174670\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6110a-26622\right){x}+269490a+1174670$
18.1-c2 18.1-c \(\Q(\sqrt{19}) \) \( 2 \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.269111170$ $2.572044164$ 1.746731012 \( \frac{3015980695953593}{502096953744} a + \frac{13147717480342991}{502096953744} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( -46790 a - 203942\) , \( -11366766 a - 49546594\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-46790a-203942\right){x}-11366766a-49546594$
18.1-d1 18.1-d \(\Q(\sqrt{19}) \) \( 2 \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.269111170$ $2.572044164$ 1.746731012 \( -\frac{3015980695953593}{502096953744} a + \frac{13147717480342991}{502096953744} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( 46789 a - 203942\) , \( 11366766 a - 49546594\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(46789a-203942\right){x}+11366766a-49546594$
18.1-d2 18.1-d \(\Q(\sqrt{19}) \) \( 2 \cdot 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.134555585$ $10.28817665$ 1.746731012 \( \frac{81634634531}{22674816} a + \frac{204402908939}{11337408} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( 6109 a - 26622\) , \( -269490 a + 1174670\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6109a-26622\right){x}-269490a+1174670$
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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.