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
4375.1-a2 4375.1-a $2$
$5$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
4375.1
\( 5^{4} \cdot 7 \)
\( 5^{6} \cdot 7^{2} \)
$1.92279$
$(-2a+1), (5)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$5$
5B.1.2 $1$
\( 2^{2} \)
$0.020655655$
$4.486407744$
1.120827230
\( \frac{4096}{7} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 2\) , \( -2\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+2{x}-2$
175.1-b2 175.1-b $2$
$5$
\(\Q(\sqrt{-35}) \) $2$
$[0, 1]$
175.1
\( 5^{2} \cdot 7 \)
\( 3^{12} \cdot 5^{6} \cdot 7^{2} \)
$1.92279$
$(5,a+2), (7,a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 5$
2Cn , 5B.1.3 $1$
\( 2^{3} \)
$0.155392136$
$4.486407744$
3.770888898
\( \frac{4096}{7} \)
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -2 a - 16\) , \( 14 a - 30\bigr] \) ${y}^2+{y}={x}^3+\left(-a+1\right){x}^2+\left(-2a-16\right){x}+14a-30$
49.1-b2 49.1-b $2$
$5$
\(\Q(\sqrt{70 -14 \sqrt{5}})\) $4$
$[4, 0]$
49.1
\( 7^{2} \)
\( 7^{4} \)
$11.37539$
$(-a^3-2a^2+5a+12)$
$2$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$5$
5B.1.1[2] $1$
\( 2 \)
$0.266156678$
$683.1012024$
2.973578042
\( \frac{4096}{7} \)
\( \bigl[0\) , \( a^{3} + a^{2} - 6 a - 3\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}+\left(a^{3}+a^{2}-6a-3\right){x}^{2}+{x}$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
