Elliptic curve search results

Results (4 matches)

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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
75.2-a1	75.2-a	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	75.2	\( 3 \cdot 5^{2} \)	\( - 3^{12} \cdot 5^{4} \)	$0.94815$	$(-a+1), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$1$	$4.872568833$	1.351407444	\( -\frac{17595448351793}{13286025} a + \frac{13466888834902}{4428675} \)	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 52 a - 125\) , \( -275 a + 631\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(52a-125\right){x}-275a+631$
225.3-c1	225.3-c	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	225.3	\( 3^{2} \cdot 5^{2} \)	\( - 3^{18} \cdot 5^{4} \)	$1.24783$	$(-a+1), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	\( 2^{3} \)	$1$	$1.149498596$	0.637627096	\( -\frac{17595448351793}{13286025} a + \frac{13466888834902}{4428675} \)	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 281 a - 660\) , \( 3632 a - 8378\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(281a-660\right){x}+3632a-8378$
675.1-g1	675.1-g	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	675.1	\( 3^{3} \cdot 5^{2} \)	\( - 3^{18} \cdot 5^{4} \)	$1.64224$	$(-a), (-a+1), (5)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	\( 2^{4} \cdot 3 \)	$0.452242980$	$8.209361925$	2.745859383	\( -\frac{17595448351793}{13286025} a + \frac{13466888834902}{4428675} \)	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 83 a - 219\) , \( -684 a + 1625\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(83a-219\right){x}-684a+1625$
1875.2-d1	1875.2-d	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	1875.2	\( 3 \cdot 5^{4} \)	\( - 3^{12} \cdot 5^{16} \)	$2.12012$	$(-a+1), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \cdot 3 \)	$0.469911852$	$0.974513766$	3.048203401	\( -\frac{17595448351793}{13286025} a + \frac{13466888834902}{4428675} \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1304 a - 3138\) , \( -34895 a + 79693\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1304a-3138\right){x}-34895a+79693$

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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.