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
11.3-a1 11.3-a $1$
$1$
4.4.12725.1 $4$
$[4, 0]$
11.3
\( 11 \)
\( 11^{8} \)
$13.60321$
$(a^2-2a-4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 2 \)
$1$
$96.18557875$
1.705340328
\( -\frac{53439337193996624}{214358881} a^{3} + \frac{195266825750471832}{214358881} a^{2} + \frac{211835797218544280}{214358881} a - \frac{938619274894806665}{214358881} \)
\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 6 a + 6\) , \( a^{2} - 6\) , \( 29 a^{3} + 14 a^{2} - 237 a - 288\) , \( 167 a^{3} + 99 a^{2} - 1368 a - 1772\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{3}-2a^{2}-6a+6\right){x}^{2}+\left(29a^{3}+14a^{2}-237a-288\right){x}+167a^{3}+99a^{2}-1368a-1772$
11.3-b1 11.3-b $1$
$1$
4.4.12725.1 $4$
$[4, 0]$
11.3
\( 11 \)
\( 11^{2} \)
$13.60321$
$(a^2-2a-4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 2 \)
$0.043622373$
$902.5690851$
2.792227723
\( -\frac{97207194933}{121} a^{3} - \frac{108939591437}{121} a^{2} + \frac{632105677974}{121} a + \frac{903328964774}{121} \)
\( \bigl[a^{2} - a - 6\) , \( a^{3} - 8 a - 6\) , \( a^{3} - 6 a - 6\) , \( -16 a^{3} + 49 a^{2} + 72 a - 219\) , \( -50 a^{3} + 189 a^{2} + 191 a - 924\bigr] \) ${y}^2+\left(a^{2}-a-6\right){x}{y}+\left(a^{3}-6a-6\right){y}={x}^{3}+\left(a^{3}-8a-6\right){x}^{2}+\left(-16a^{3}+49a^{2}+72a-219\right){x}-50a^{3}+189a^{2}+191a-924$
11.3-c1 11.3-c $1$
$1$
4.4.12725.1 $4$
$[4, 0]$
11.3
\( 11 \)
\( 11^{4} \)
$13.60321$
$(a^2-2a-4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 2^{2} \)
$0.050271146$
$384.8036971$
2.743778882
\( -\frac{195271897}{14641} a^{3} - \frac{210506526}{14641} a^{2} + \frac{1254806474}{14641} a + \frac{1760694200}{14641} \)
\( \bigl[a^{2} - a - 5\) , \( a^{3} - 8 a - 5\) , \( a^{3} - a^{2} - 5 a + 1\) , \( -3 a^{3} + 4 a^{2} + 14 a + 4\) , \( -4 a^{3} + 11 a^{2} + 11 a - 29\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{3}-a^{2}-5a+1\right){y}={x}^{3}+\left(a^{3}-8a-5\right){x}^{2}+\left(-3a^{3}+4a^{2}+14a+4\right){x}-4a^{3}+11a^{2}+11a-29$
11.3-d1 11.3-d $2$
$3$
4.4.12725.1 $4$
$[4, 0]$
11.3
\( 11 \)
\( 11^{6} \)
$13.60321$
$(a^2-2a-4)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.1 $1$
\( 2 \cdot 3 \)
$0.848760694$
$142.5873199$
2.860921903
\( -\frac{24388973560}{1771561} a^{3} - \frac{17420952534}{1771561} a^{2} + \frac{202430910278}{1771561} a + \frac{275090744229}{1771561} \)
\( \bigl[a^{2} - a - 5\) , \( a^{3} - 8 a - 6\) , \( a^{2} - a - 5\) , \( -3 a^{3} - 3 a^{2} + 24 a + 36\) , \( a^{3} - 10 a - 12\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{3}-8a-6\right){x}^{2}+\left(-3a^{3}-3a^{2}+24a+36\right){x}+a^{3}-10a-12$
11.3-d2 11.3-d $2$
$3$
4.4.12725.1 $4$
$[4, 0]$
11.3
\( 11 \)
\( 11^{2} \)
$13.60321$
$(a^2-2a-4)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.2 $9$
\( 2 \)
$2.546282084$
$1.760337283$
2.860921903
\( -\frac{28643793854842421}{121} a^{3} - \frac{18681629188709988}{121} a^{2} + \frac{236890417776297407}{121} a + \frac{313199971597619969}{121} \)
\( \bigl[a^{2} - a - 5\) , \( a^{3} - 8 a - 6\) , \( a^{2} - a - 5\) , \( -58 a^{3} - 53 a^{2} + 359 a + 436\) , \( -641 a^{3} - 660 a^{2} + 4121 a + 5573\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{3}-8a-6\right){x}^{2}+\left(-58a^{3}-53a^{2}+359a+436\right){x}-641a^{3}-660a^{2}+4121a+5573$
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Pari/GP
SageMath
Magma
Oscar
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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.
