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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
2025.1-a1 2025.1-a \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.025588090$ $7.268178697$ 1.996134097 \( -\frac{102400}{3} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -75\) , \( 256\bigr] \) ${y}^2+{y}={x}^{3}-75{x}+256$
2025.1-a2 2025.1-a \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.127940452$ $1.453635739$ 1.996134097 \( \frac{20480}{243} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 15\) , \( -99\bigr] \) ${y}^2+{y}={x}^{3}+15{x}-99$
2025.1-b1 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.018276957$ 2.092468141 \( -\frac{152409672113485069453847362}{45} a + \frac{246604029693845863366701161}{45} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 151875 \phi - 500175\) , \( 56696050 \phi - 141391500\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(151875\phi-500175\right){x}+56696050\phi-141391500$
2025.1-b2 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.073107828$ 2.092468141 \( -\frac{147281603041}{215233605} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -4950 \phi - 4950\) , \( -455300 \phi - 341475\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-4950\phi-4950\right){x}-455300\phi-341475$
2025.1-b3 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $4.678901004$ 2.092468141 \( -\frac{1}{15} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 0\) , \( 100 \phi + 75\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+100\phi+75$
2025.1-b4 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.292431312$ 2.092468141 \( \frac{4733169839}{3515625} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 1575 \phi + 1575\) , \( -21320 \phi - 15990\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(1575\phi+1575\right){x}-21320\phi-15990$
2025.1-b5 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.169725251$ 2.092468141 \( \frac{111284641}{50625} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -450 \phi - 450\) , \( -3500 \phi - 2625\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-450\phi-450\right){x}-3500\phi-2625$
2025.1-b6 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.678901004$ 2.092468141 \( \frac{13997521}{225} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -225 \phi - 225\) , \( 2080 \phi + 1560\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-225\phi-225\right){x}+2080\phi+1560$
2025.1-b7 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.292431312$ 2.092468141 \( \frac{272223782641}{164025} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -6075 \phi - 6075\) , \( -332000 \phi - 249000\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-6075\phi-6075\right){x}-332000\phi-249000$
2025.1-b8 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $4.678901004$ 2.092468141 \( \frac{56667352321}{15} \) \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( 3601 \phi - 7202\) , \( -148781 \phi + 261266\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(3601\phi-7202\right){x}-148781\phi+261266$
2025.1-b9 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.073107828$ 2.092468141 \( \frac{1114544804970241}{405} \) \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( -97200 \phi - 97200\) , \( -20962700 \phi - 15722025\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-97200\phi-97200\right){x}-20962700\phi-15722025$
2025.1-b10 2025.1-b \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.018276957$ 2.092468141 \( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \) \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( -151874 \phi - 348302\) , \( -56544176 \phi - 84347149\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-151874\phi-348302\right){x}-56544176\phi-84347149$
2025.1-c1 2025.1-c \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\mathsf{trivial}$ $-3$ $1$ $2.448734813$ 2.190215000 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -25 \phi - 19\bigr] \) ${y}^2+{y}={x}^{3}-25\phi-19$
2025.1-c2 2025.1-c \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\mathsf{trivial}$ $-3$ $1$ $2.448734813$ 2.190215000 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 675 \phi + 506\bigr] \) ${y}^2+{y}={x}^{3}+675\phi+506$
2025.1-d1 2025.1-d \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $1$ $\Z/3\Z$ $-3$ $0.153640035$ $16.42661250$ 1.504894809 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 1\bigr] \) ${y}^2+{y}={x}^{3}+1$
2025.1-d2 2025.1-d \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $-3$ $0.460920105$ $1.825179167$ 1.504894809 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -34\bigr] \) ${y}^2+{y}={x}^{3}-34$
2025.1-e1 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $-15$ $1$ $3.521839301$ 1.575014416 \( -85995 a - 52515 \) \( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -6 \phi + 6\) , \( -7 \phi + 10\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-6\phi+6\right){x}-7\phi+10$
2025.1-e2 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $-15$ $1$ $3.521839301$ 1.575014416 \( -85995 a - 52515 \) \( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -59 \phi + 51\) , \( 253 \phi - 264\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-59\phi+51\right){x}+253\phi-264$
2025.1-e3 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $-15$ $1$ $3.521839301$ 1.575014416 \( 85995 a - 138510 \) \( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 6 \phi - 1\) , \( 13 \phi + 2\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(6\phi-1\right){x}+13\phi+2$
2025.1-e4 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $-15$ $1$ $3.521839301$ 1.575014416 \( 85995 a - 138510 \) \( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( 59 \phi - 8\) , \( -194 \phi - 19\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(59\phi-8\right){x}-194\phi-19$
2025.1-e5 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $-60$ $1$ $3.521839301$ 1.575014416 \( -16554983445 a + 26786530035 \) \( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 6 \phi - 76\) , \( 178 \phi - 193\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(6\phi-76\right){x}+178\phi-193$
2025.1-e6 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $-60$ $1$ $3.521839301$ 1.575014416 \( -16554983445 a + 26786530035 \) \( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( 59 \phi - 683\) , \( -5324 \phi + 3896\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+{x}^{2}+\left(59\phi-683\right){x}-5324\phi+3896$
2025.1-e7 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $-60$ $1$ $3.521839301$ 1.575014416 \( 16554983445 a + 10231546590 \) \( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -6 \phi - 69\) , \( -172 \phi + 55\bigr] \) ${y}^2+\phi{x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-6\phi-69\right){x}-172\phi+55$
2025.1-e8 2025.1-e \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\Z/2\Z$ $-60$ $1$ $3.521839301$ 1.575014416 \( 16554983445 a + 10231546590 \) \( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -59 \phi - 624\) , \( 5383 \phi - 804\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-59\phi-624\right){x}+5383\phi-804$
2025.1-f1 2025.1-f \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\mathsf{trivial}$ $1$ $1.466203400$ 1.311412189 \( -\frac{102400}{3} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -15 \phi - 15\) , \( -41 \phi - 31\bigr] \) ${y}^2+{y}={x}^{3}+\left(-15\phi-15\right){x}-41\phi-31$
2025.1-f2 2025.1-f \(\Q(\sqrt{5}) \) \( 3^{4} \cdot 5^{2} \) $0$ $\mathsf{trivial}$ $1$ $1.466203400$ 1.311412189 \( \frac{20480}{243} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -75 \phi + 150\) , \( -1975 \phi + 3456\bigr] \) ${y}^2+{y}={x}^{3}+\left(-75\phi+150\right){x}-1975\phi+3456$
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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.