| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 37570.10-a1 |
37570.10-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{3} \cdot 5^{2} \cdot 13^{4} \cdot 17^{8} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.801502173$ |
$0.541869694$ |
3.474477905 |
\( \frac{3398703313}{2856100} a - \frac{8758858759}{2856100} \) |
\( \bigl[i\) , \( -i + 1\) , \( i\) , \( -123 i - 133\) , \( -1048 i - 514\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-123i-133\right){x}-1048i-514$ |
| 37570.10-b1 |
37570.10-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{3} \cdot 5^{10} \cdot 13^{2} \cdot 17^{7} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.342965045$ |
$0.306361231$ |
4.937189107 |
\( \frac{3168051468697443}{112226562500} a - \frac{4949489622009749}{112226562500} \) |
\( \bigl[i\) , \( -i\) , \( i\) , \( 1033 i - 14\) , \( -9506 i - 8543\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(1033i-14\right){x}-9506i-8543$ |
| 37570.10-b2 |
37570.10-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{6} \cdot 5^{5} \cdot 13 \cdot 17^{8} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.671482522$ |
$0.612722463$ |
4.937189107 |
\( \frac{32301205361}{93925000} a + \frac{1823254619}{11740625} \) |
\( \bigl[i\) , \( -i\) , \( i\) , \( 43 i - 64\) , \( 14 i - 519\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(43i-64\right){x}+14i-519$ |
| 37570.10-c1 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{18} \cdot 5^{9} \cdot 13 \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$0.079352997$ |
$0.233010375$ |
5.990783243 |
\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 1744 i + 39\) , \( 20027 i + 21608\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(1744i+39\right){x}+20027i+21608$ |
| 37570.10-c2 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{6} \cdot 5^{3} \cdot 13^{3} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.238058992$ |
$0.699031126$ |
5.990783243 |
\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 104 i - 146\) , \( -666 i + 546\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(104i-146\right){x}-666i+546$ |
| 37570.10-c3 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{3} \cdot 5^{6} \cdot 13^{6} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.476117985$ |
$0.349515563$ |
5.990783243 |
\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( -126 i - 216\) , \( -2996 i - 716\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-126i-216\right){x}-2996i-716$ |
| 37570.10-c4 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{9} \cdot 5^{18} \cdot 13^{2} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$0.158705995$ |
$0.116505187$ |
5.990783243 |
\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( 1184 i + 1879\) , \( 78699 i - 744\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(1184i+1879\right){x}+78699i-744$ |
| 37570.10-c5 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{2} \cdot 5 \cdot 13 \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.714176977$ |
$2.097093378$ |
5.990783243 |
\( \frac{31409}{130} a + \frac{101344}{65} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( -6 i + 9\) , \( -11 i + 4\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-6i+9\right){x}-11i+4$ |
| 37570.10-c6 |
37570.10-c |
$6$ |
$18$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2 \cdot 5^{2} \cdot 13^{2} \cdot 17^{6} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.428353955$ |
$1.048546689$ |
5.990783243 |
\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) |
\( \bigl[1\) , \( -i + 1\) , \( i + 1\) , \( -41 i + 124\) , \( -572 i - 217\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-41i+124\right){x}-572i-217$ |
| 37570.10-d1 |
37570.10-d |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
37570.10 |
\( 2 \cdot 5 \cdot 13 \cdot 17^{2} \) |
\( 2^{3} \cdot 5^{2} \cdot 13^{4} \cdot 17^{2} \) |
$2.48816$ |
$(a+1), (2a+1), (2a+3), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.052381765$ |
$2.234185987$ |
5.617469102 |
\( \frac{3398703313}{2856100} a - \frac{8758858759}{2856100} \) |
\( \bigl[i\) , \( i\) , \( 1\) , \( 2 i + 10\) , \( 18 i - 9\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(2i+10\right){x}+18i-9$ |
*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.
