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Results (16 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
2.1-a1 2.1-a \(\Q(\sqrt{114}) \) \( 2 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.234562170$ $0.872145222$ 5.130952434 \( -\frac{216595158866073603}{4} a + 578150865056023272 \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 65568 a - 700075\) , \( 29846182 a - 318670021\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(65568a-700075\right){x}+29846182a-318670021$
2.1-a2 2.1-a \(\Q(\sqrt{114}) \) \( 2 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $5.234562170$ $13.95432355$ 5.130952434 \( \frac{2146689}{64} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 258 a - 2755\) , \( 7114 a - 75957\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(258a-2755\right){x}+7114a-75957$
2.1-a3 2.1-a \(\Q(\sqrt{114}) \) \( 2 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $10.46912434$ $3.488580888$ 5.130952434 \( \frac{8602523649}{8} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 4098 a - 43755\) , \( 465578 a - 4971013\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(4098a-43755\right){x}+465578a-4971013$
2.1-a4 2.1-a \(\Q(\sqrt{114}) \) \( 2 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $20.93824868$ $0.872145222$ 5.130952434 \( \frac{216595158866073603}{4} a + 578150865056023272 \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 4068 a - 43435\) , \( 472750 a - 5047589\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(4068a-43435\right){x}+472750a-5047589$
2.1-b1 2.1-b \(\Q(\sqrt{114}) \) \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $19.10792981$ 0.894810797 \( -\frac{216595158866073603}{4} a + 578150865056023272 \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 590112 a - 6300672\) , \( -806437026 a + 8610391232\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(590112a-6300672\right){x}-806437026a+8610391232$
2.1-b2 2.1-b \(\Q(\sqrt{114}) \) \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $38.21585963$ 0.894810797 \( \frac{2146689}{64} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 2322 a - 24792\) , \( -194400 a + 2075624\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(2322a-24792\right){x}-194400a+2075624$
2.1-b3 2.1-b \(\Q(\sqrt{114}) \) \( 2 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $38.21585963$ 0.894810797 \( \frac{8602523649}{8} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 36882 a - 393792\) , \( -12607488 a + 134611136\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(36882a-393792\right){x}-12607488a+134611136$
2.1-b4 2.1-b \(\Q(\sqrt{114}) \) \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $19.10792981$ 0.894810797 \( \frac{216595158866073603}{4} a + 578150865056023272 \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 36612 a - 390912\) , \( -12800862 a + 136675808\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(36612a-390912\right){x}-12800862a+136675808$
2.1-c1 2.1-c \(\Q(\sqrt{114}) \) \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $19.10792981$ 0.894810797 \( -\frac{216595158866073603}{4} a + 578150865056023272 \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -36612 a - 390912\) , \( 12800862 a + 136675808\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-36612a-390912\right){x}+12800862a+136675808$
2.1-c2 2.1-c \(\Q(\sqrt{114}) \) \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $38.21585963$ 0.894810797 \( \frac{2146689}{64} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -2322 a - 24792\) , \( 194400 a + 2075624\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-2322a-24792\right){x}+194400a+2075624$
2.1-c3 2.1-c \(\Q(\sqrt{114}) \) \( 2 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $38.21585963$ 0.894810797 \( \frac{8602523649}{8} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -36882 a - 393792\) , \( 12607488 a + 134611136\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-36882a-393792\right){x}+12607488a+134611136$
2.1-c4 2.1-c \(\Q(\sqrt{114}) \) \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $19.10792981$ 0.894810797 \( \frac{216595158866073603}{4} a + 578150865056023272 \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -590112 a - 6300672\) , \( 806437026 a + 8610391232\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-590112a-6300672\right){x}+806437026a+8610391232$
2.1-d1 2.1-d \(\Q(\sqrt{114}) \) \( 2 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $20.93824868$ $0.872145222$ 5.130952434 \( -\frac{216595158866073603}{4} a + 578150865056023272 \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -4068 a - 43435\) , \( -472750 a - 5047589\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-4068a-43435\right){x}-472750a-5047589$
2.1-d2 2.1-d \(\Q(\sqrt{114}) \) \( 2 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $5.234562170$ $13.95432355$ 5.130952434 \( \frac{2146689}{64} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -258 a - 2755\) , \( -7114 a - 75957\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-258a-2755\right){x}-7114a-75957$
2.1-d3 2.1-d \(\Q(\sqrt{114}) \) \( 2 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $10.46912434$ $3.488580888$ 5.130952434 \( \frac{8602523649}{8} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -4098 a - 43755\) , \( -465578 a - 4971013\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-4098a-43755\right){x}-465578a-4971013$
2.1-d4 2.1-d \(\Q(\sqrt{114}) \) \( 2 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.234562170$ $0.872145222$ 5.130952434 \( \frac{216595158866073603}{4} a + 578150865056023272 \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -65568 a - 700075\) , \( -29846182 a - 318670021\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-65568a-700075\right){x}-29846182a-318670021$
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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.