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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
50625.3-CMf1 50625.3-CMf \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $0$ $\Z/2\Z$ $-4$ $1$ $0.791416409$ 3.165665637 \( 1728 \) \( \bigl[i + 1\) , \( i\) , \( 1\) , \( 67 i - 35\) , \( -17 i - 34\bigr] \) ${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(67i-35\right){x}-17i-34$
50625.3-CMe1 50625.3-CMe \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $0$ $\Z/2\Z$ $-4$ $1$ $0.791416409$ 3.165665637 \( 1728 \) \( \bigl[i + 1\) , \( i\) , \( i\) , \( -68 i - 34\) , \( -17 i + 34\bigr] \) ${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-68i-34\right){x}-17i+34$
50625.3-CMd1 50625.3-CMd \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $0$ $\Z/2\Z$ $-4$ $1$ $0.613028514$ 1.226057029 \( 1728 \) \( \bigl[i + 1\) , \( i\) , \( 1\) , \( -113 i + 55\) , \( 28 i + 56\bigr] \) ${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-113i+55\right){x}+28i+56$
50625.3-CMc1 50625.3-CMc \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $0$ $\Z/2\Z$ $-4$ $1$ $0.613028514$ 1.226057029 \( 1728 \) \( \bigl[i + 1\) , \( i\) , \( i\) , \( 112 i + 56\) , \( 28 i - 56\bigr] \) ${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(112i+56\right){x}+28i-56$
50625.3-CMb1 50625.3-CMb \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $2$ $\Z/2\Z$ $-4$ $0.081821379$ $2.374249228$ 3.108229546 \( 1728 \) \( \bigl[i + 1\) , \( i\) , \( 1\) , \( 7 i - 5\) , \( -2 i - 4\bigr] \) ${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(7i-5\right){x}-2i-4$
50625.3-CMa1 50625.3-CMa \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $2$ $\Z/2\Z$ $-4$ $0.081821379$ $2.374249228$ 3.108229546 \( 1728 \) \( \bigl[i + 1\) , \( i\) , \( i\) , \( -8 i - 4\) , \( -2 i + 4\bigr] \) ${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-8i-4\right){x}-2i+4$
50625.3-a1 50625.3-a \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $0.025588090$ $1.091534363$ 2.010980162 \( -\frac{102400}{3} \) \( \bigl[0\) , \( 0\) , \( i\) , \( -75\) , \( -256\bigr] \) ${y}^2+i{y}={x}^{3}-75{x}-256$
50625.3-a2 50625.3-a \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $0.127940452$ $0.218306872$ 2.010980162 \( \frac{20480}{243} \) \( \bigl[0\) , \( 0\) , \( i\) , \( 375\) , \( 12344\bigr] \) ${y}^2+i{y}={x}^{3}+375{x}+12344$
50625.3-b1 50625.3-b \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $2.400975354$ $0.037261695$ 2.862861179 \( -\frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) \( \bigl[i\) , \( 1\) , \( i\) , \( -23625 i + 88871\) , \( -9922500 i - 4089872\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(-23625i+88871\right){x}-9922500i-4089872$
50625.3-b2 50625.3-b \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $2.400975354$ $0.037261695$ 2.862861179 \( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) \( \bigl[i\) , \( 1\) , \( i\) , \( 23625 i + 88871\) , \( 9922500 i - 4089872\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(23625i+88871\right){x}+9922500i-4089872$
50625.3-b3 50625.3-b \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $9.603901418$ $0.037261695$ 2.862861179 \( -\frac{147281603041}{215233605} \) \( \bigl[i\) , \( 1\) , \( i\) , \( -24754\) , \( -2820872\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-24754{x}-2820872$
50625.3-b4 50625.3-b \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/4\Z$ $0.600243838$ $0.596187123$ 2.862861179 \( -\frac{1}{15} \) \( \bigl[i\) , \( 1\) , \( i\) , \( -4\) , \( 628\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-4{x}+628$
50625.3-b5 50625.3-b \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $4.801950709$ $0.074523390$ 2.862861179 \( \frac{4733169839}{3515625} \) \( \bigl[i\) , \( 1\) , \( i\) , \( 7871\) , \( -141122\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+7871{x}-141122$
50625.3-b6 50625.3-b \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $2.400975354$ $0.149046780$ 2.862861179 \( \frac{111284641}{50625} \) \( \bigl[i\) , \( 1\) , \( i\) , \( -2254\) , \( -19622\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-2254{x}-19622$
50625.3-b7 50625.3-b \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.200487677$ $0.298093561$ 2.862861179 \( \frac{13997521}{225} \) \( \bigl[i\) , \( 1\) , \( i\) , \( -1129\) , \( 14128\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-1129{x}+14128$
50625.3-b8 50625.3-b \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $4.801950709$ $0.074523390$ 2.862861179 \( \frac{272223782641}{164025} \) \( \bigl[i\) , \( 1\) , \( i\) , \( -30379\) , \( -2044622\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-30379{x}-2044622$
50625.3-b9 50625.3-b \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/4\Z$ $2.400975354$ $0.149046780$ 2.862861179 \( \frac{56667352321}{15} \) \( \bigl[i\) , \( 1\) , \( i\) , \( -18004\) , \( 925378\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-18004{x}+925378$
50625.3-b10 50625.3-b \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $9.603901418$ $0.037261695$ 2.862861179 \( \frac{1114544804970241}{405} \) \( \bigl[i\) , \( 1\) , \( i\) , \( -486004\) , \( -130530872\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-486004{x}-130530872$
50625.3-c1 50625.3-c \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $0.460920105$ $1.580651525$ 2.914216267 \( 0 \) \( \bigl[0\) , \( 0\) , \( i\) , \( 0\) , \( 34\bigr] \) ${y}^2+i{y}={x}^{3}+34$
50625.3-c2 50625.3-c \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $0.153640035$ $4.741954575$ 2.914216267 \( 0 \) \( \bigl[0\) , \( 0\) , \( i\) , \( 0\) , \( -1\bigr] \) ${y}^2+i{y}={x}^{3}-1$
50625.3-d1 50625.3-d \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $1.897634689$ $0.207768522$ 3.154150045 \( -\frac{8722944}{125} a - \frac{10158912}{125} \) \( \bigl[i + 1\) , \( i\) , \( i\) , \( -338 i + 2531\) , \( -47672 i - 9956\bigr] \) ${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-338i+2531\right){x}-47672i-9956$
50625.3-d2 50625.3-d \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $0.316272448$ $0.623305567$ 3.154150045 \( \frac{8722944}{125} a - \frac{10158912}{125} \) \( \bigl[i + 1\) , \( i\) , \( 1\) , \( 37 i + 280\) , \( 1953 i - 394\bigr] \) ${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(37i+280\right){x}+1953i-394$
50625.3-d3 50625.3-d \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $0.632544896$ $0.623305567$ 3.154150045 \( -\frac{5792256}{15625} a + \frac{13929408}{15625} \) \( \bigl[i + 1\) , \( i\) , \( i\) , \( 37 i - 94\) , \( -422 i - 81\bigr] \) ${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(37i-94\right){x}-422i-81$
50625.3-d4 50625.3-d \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $0.948817344$ $0.207768522$ 3.154150045 \( \frac{5792256}{15625} a + \frac{13929408}{15625} \) \( \bigl[i + 1\) , \( i\) , \( 1\) , \( -338 i - 845\) , \( 9703 i - 1519\bigr] \) ${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-338i-845\right){x}+9703i-1519$
50625.3-e1 50625.3-e \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $0.316272448$ $0.623305567$ 3.154150045 \( -\frac{8722944}{125} a - \frac{10158912}{125} \) \( \bigl[i + 1\) , \( i\) , \( i\) , \( -38 i + 281\) , \( -1672 i - 356\bigr] \) ${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-38i+281\right){x}-1672i-356$
50625.3-e2 50625.3-e \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $1.897634689$ $0.207768522$ 3.154150045 \( \frac{8722944}{125} a - \frac{10158912}{125} \) \( \bigl[i + 1\) , \( i\) , \( 1\) , \( 337 i + 2530\) , \( -47672 i + 9956\bigr] \) ${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(337i+2530\right){x}-47672i+9956$
50625.3-e3 50625.3-e \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $0.948817344$ $0.207768522$ 3.154150045 \( -\frac{5792256}{15625} a + \frac{13929408}{15625} \) \( \bigl[i + 1\) , \( i\) , \( i\) , \( 337 i - 844\) , \( -10547 i - 1856\bigr] \) ${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(337i-844\right){x}-10547i-1856$
50625.3-e4 50625.3-e \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/2\Z$ $0.632544896$ $0.623305567$ 3.154150045 \( \frac{5792256}{15625} a + \frac{13929408}{15625} \) \( \bigl[i + 1\) , \( i\) , \( 1\) , \( -38 i - 95\) , \( -422 i + 81\bigr] \) ${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-38i-95\right){x}-422i+81$
50625.3-f1 50625.3-f \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\Z/3\Z$ $-3$ $1.007478452$ $0.948390915$ 3.821933646 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 156\bigr] \) ${y}^2+{y}={x}^{3}+156$
50625.3-f2 50625.3-f \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $3.022435358$ $0.316130305$ 3.821933646 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -4219\bigr] \) ${y}^2+{y}={x}^{3}-4219$
50625.3-g1 50625.3-g \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $4.591654055$ $0.218306872$ 8.019117100 \( -\frac{102400}{3} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -1875\) , \( 32031\bigr] \) ${y}^2+{y}={x}^{3}-1875{x}+32031$
50625.3-g2 50625.3-g \(\Q(\sqrt{-1}) \) \( 3^{4} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $0.918330811$ $1.091534363$ 8.019117100 \( \frac{20480}{243} \) \( \bigl[0\) , \( 0\) , \( i\) , \( 15\) , \( 99\bigr] \) ${y}^2+i{y}={x}^{3}+15{x}+99$
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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.