| 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 |
| 124.1-a3 |
124.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{10} \cdot 31^{5} \) |
$0.51648$ |
$(-6a+1), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5Cs.1.1 |
$1$ |
\( 5 \) |
$1$ |
$1.842158930$ |
0.425428381 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -15 a + 5\) , \( -7 a + 21\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-15a+5\right){x}-7a+21$ |
| 7936.1-c3 |
7936.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.1 |
\( 2^{8} \cdot 31 \) |
\( 2^{34} \cdot 31^{5} \) |
$1.46083$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \) |
$0.576472224$ |
$0.460539732$ |
2.452476457 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -240 a + 88\) , \( 128 a - 860\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-240a+88\right){x}+128a-860$ |
| 20956.1-c1 |
20956.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20956.1 |
\( 2^{2} \cdot 13^{2} \cdot 31 \) |
\( 2^{10} \cdot 13^{6} \cdot 31^{5} \) |
$1.86220$ |
$(-4a+1), (-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 5 \) |
$1$ |
$0.510922960$ |
2.949815085 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -186 a + 149\) , \( 284 a + 375\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-186a+149\right){x}+284a+375$ |
| 20956.5-b1 |
20956.5-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20956.5 |
\( 2^{2} \cdot 13^{2} \cdot 31 \) |
\( 2^{10} \cdot 13^{6} \cdot 31^{5} \) |
$1.86220$ |
$(4a-3), (-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5^{2} \) |
$0.055752934$ |
$0.510922960$ |
3.289216924 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 180 a - 159\) , \( -507 a + 550\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(180a-159\right){x}-507a+550$ |
| 34596.1-d1 |
34596.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
34596.1 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 31^{11} \) |
$2.11084$ |
$(-2a+1), (-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.191022982$ |
2.205743407 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -502 a + 1395\) , \( 11605 a - 9356\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-502a+1395\right){x}+11605a-9356$ |
| 54684.1-d1 |
54684.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54684.1 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 31 \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{6} \cdot 31^{5} \) |
$2.36681$ |
$(-2a+1), (-3a+1), (-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 5 \) |
$1$ |
$0.401992035$ |
2.320902097 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -276 a - 3\) , \( 770 a - 1373\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-276a-3\right){x}+770a-1373$ |
| 54684.5-d1 |
54684.5-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54684.5 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 31 \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{6} \cdot 31^{5} \) |
$2.36681$ |
$(-2a+1), (3a-2), (-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5^{2} \) |
$0.084171321$ |
$0.401992035$ |
3.907067914 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -312 a + 219\) , \( -476 a - 759\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-312a+219\right){x}-476a-759$ |
| 71424.1-a1 |
71424.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.1 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{34} \cdot 3^{6} \cdot 31^{5} \) |
$2.53023$ |
$(-2a+1), (-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \) |
$1.401922107$ |
$0.265892738$ |
3.443417772 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -264 a - 456\) , \( 4776 a - 1812\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-264a-456\right){x}+4776a-1812$ |
| 71424.1-h1 |
71424.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.1 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{34} \cdot 3^{6} \cdot 31^{5} \) |
$2.53023$ |
$(-2a+1), (-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.265892738$ |
3.070264883 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -455 a + 721\) , \( -4511 a + 2268\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-455a+721\right){x}-4511a+2268$ |
| 77500.1-b1 |
77500.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.1 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{10} \cdot 5^{12} \cdot 31^{5} \) |
$2.58241$ |
$(-6a+1), (2), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.1.3 |
$1$ |
\( 5 \) |
$1$ |
$0.368431786$ |
2.127141908 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 137 a + 238\) , \( -132 a + 1492\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(137a+238\right){x}-132a+1492$ |
| 126976.1-c1 |
126976.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{46} \cdot 31^{5} \) |
$2.92166$ |
$(-6a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2^{2} \) |
$1.752654364$ |
$0.230269866$ |
3.728144549 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -961 a + 353\) , \( 416 a - 5919\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-961a+353\right){x}+416a-5919$ |
| 126976.1-h1 |
126976.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.1 |
\( 2^{12} \cdot 31 \) |
\( 2^{46} \cdot 31^{5} \) |
$2.92166$ |
$(-6a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.230269866$ |
2.658927385 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 608 a - 961\) , \( -416 a + 5919\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(608a-961\right){x}-416a+5919$ |
*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.
