Elliptic curves over $\Q$ of conductor 378

Results (16 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
378.a1	378h1	378.a	378h	$1$	$1$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{5} \cdot 3^{5} \cdot 7^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$168$	$2$	$0$	$1$	$1$		$0$	$420$	$0.570366$	$38983348653/26353376$	$1.05350$	$5.03454$	$[1, -1, 0, 441, -1571]$	\(y^2+xy=x^3-x^2+441x-1571\)	168.2.0.?	$[]$
378.b1	378f1	378.b	378f	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{2} \cdot 3^{3} \cdot 7 \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.1	3B.1.1	$252$	$144$	$3$	$1.302973442$	$1$		$6$	$72$	$-0.207361$	$-11527859979/28$	$1.03505$	$4.45903$	$[1, -1, 0, -141, 681]$	\(y^2+xy=x^3-x^2-141x+681\)	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 63.72.0-63.f.2.2, 84.16.0.?, 252.144.3.?	$[(4, 11)]$
378.b2	378f2	378.b	378f	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{6} \cdot 3^{9} \cdot 7^{3} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.24.0.1	3Cs.1.1	$252$	$144$	$3$	$0.434324480$	$1$		$14$	$216$	$0.341945$	$-5000211/21952$	$1.03310$	$4.62732$	$[1, -1, 0, -96, 1088]$	\(y^2+xy=x^3-x^2-96x+1088\)	3.24.0-3.a.1.1, 63.72.0-63.c.1.1, 84.48.1.?, 252.144.3.?	$[(8, 24)]$
378.b3	378f3	378.b	378f	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{18} \cdot 3^{11} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.3	3B.1.2	$252$	$144$	$3$	$1.302973442$	$1$		$2$	$648$	$0.891252$	$381790581/1835008$	$1.02442$	$5.70081$	$[1, -1, 0, 849, -25939]$	\(y^2+xy=x^3-x^2+849x-25939\)	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 63.72.0-63.f.1.3, 84.16.0.?, 252.144.3.?	$[(62, 481)]$
378.c1	378d1	378.c	378d	$1$	$1$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{2} \cdot 3^{5} \cdot 7 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$84$	$2$	$0$	$0.064494142$	$1$		$10$	$24$	$-0.585649$	$-3/28$	$1.12894$	$2.74311$	$[1, -1, 0, 0, 4]$	\(y^2+xy=x^3-x^2+4\)	84.2.0.?	$[(2, 2)]$
378.d1	378b3	378.d	378b	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2 \cdot 3^{5} \cdot 7 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.1	3B.1.1	$504$	$144$	$3$	$1$	$1$		$2$	$108$	$0.193884$	$-545407363875/14$	$1.02302$	$5.47910$	$[1, -1, 0, -1062, 13590]$	\(y^2+xy=x^3-x^2-1062x+13590\)	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 63.72.0-63.d.2.4, 168.16.0.?, 504.144.3.?	$[]$
378.d2	378b1	378.d	378b	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{3} \cdot 3^{3} \cdot 7^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.24.0.1	3Cs.1.1	$504$	$144$	$3$	$1$	$1$		$2$	$36$	$-0.355422$	$-7414875/2744$	$0.97713$	$3.30405$	$[1, -1, 0, -12, 24]$	\(y^2+xy=x^3-x^2-12x+24\)	3.24.0-3.a.1.1, 63.72.0-63.a.1.3, 168.48.1.?, 504.144.3.?	$[]$
378.d3	378b2	378.d	378b	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{9} \cdot 3^{9} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.3	3B.1.2	$504$	$144$	$3$	$1$	$1$		$0$	$108$	$0.193884$	$4492125/3584$	$1.01407$	$4.24697$	$[1, -1, 0, 93, -235]$	\(y^2+xy=x^3-x^2+93x-235\)	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 63.72.0-63.d.1.3, 168.16.0.?, 504.144.3.?	$[]$
378.e1	378a3	378.e	378a	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2 \cdot 3^{11} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.3	3B.1.2	$504$	$144$	$3$	$1$	$9$	$3$	$0$	$324$	$0.743190$	$-545407363875/14$	$1.02302$	$6.58976$	$[1, -1, 1, -9560, -357371]$	\(y^2+xy+y=x^3-x^2-9560x-357371\)	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 63.72.0-63.d.2.3, 168.16.0.?, 504.144.3.?	$[]$
378.e2	378a2	378.e	378a	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{3} \cdot 3^{9} \cdot 7^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.24.0.1	3Cs.1.1	$504$	$144$	$3$	$1$	$1$		$2$	$108$	$0.193884$	$-7414875/2744$	$0.97713$	$4.41472$	$[1, -1, 1, -110, -539]$	\(y^2+xy+y=x^3-x^2-110x-539\)	3.24.0-3.a.1.1, 63.72.0-63.a.1.1, 168.48.1.?, 504.144.3.?	$[]$
378.e3	378a1	378.e	378a	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{9} \cdot 3^{3} \cdot 7 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.1	3B.1.1	$504$	$144$	$3$	$1$	$1$		$2$	$36$	$-0.355422$	$4492125/3584$	$1.01407$	$3.13631$	$[1, -1, 1, 10, 5]$	\(y^2+xy+y=x^3-x^2+10x+5\)	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 63.72.0-63.d.1.4, 168.16.0.?, 504.144.3.?	$[]$
378.f1	378c1	378.f	378c	$1$	$1$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{2} \cdot 3^{11} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$84$	$2$	$0$	$1$	$1$		$0$	$72$	$-0.036342$	$-3/28$	$1.12894$	$3.85377$	$[1, -1, 1, -2, -107]$	\(y^2+xy+y=x^3-x^2-2x-107\)	84.2.0.?	$[]$
378.g1	378e2	378.g	378e	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{2} \cdot 3^{9} \cdot 7 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.3	3B.1.2	$252$	$144$	$3$	$1$	$1$		$0$	$216$	$0.341945$	$-11527859979/28$	$1.03505$	$5.56969$	$[1, -1, 1, -1271, -17117]$	\(y^2+xy+y=x^3-x^2-1271x-17117\)	3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 63.72.0-63.f.2.1, 84.16.0.?, 252.144.3.?	$[]$
378.g2	378e1	378.g	378e	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{6} \cdot 3^{3} \cdot 7^{3} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.24.0.1	3Cs.1.1	$252$	$144$	$3$	$1$	$1$		$2$	$72$	$-0.207361$	$-5000211/21952$	$1.03310$	$3.51666$	$[1, -1, 1, -11, -37]$	\(y^2+xy+y=x^3-x^2-11x-37\)	3.24.0-3.a.1.1, 63.72.0-63.c.1.3, 84.48.1.?, 252.144.3.?	$[]$
378.g3	378e3	378.g	378e	$3$	$9$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{18} \cdot 3^{5} \cdot 7 \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	9.24.0.1	3B.1.1	$252$	$144$	$3$	$1$	$1$		$2$	$216$	$0.341945$	$381790581/1835008$	$1.02442$	$4.59015$	$[1, -1, 1, 94, 929]$	\(y^2+xy+y=x^3-x^2+94x+929\)	3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 63.72.0-63.f.1.4, 84.16.0.?, 252.144.3.?	$[]$
378.h1	378g1	378.h	378g	$1$	$1$	\( 2 \cdot 3^{3} \cdot 7 \)	\( - 2^{5} \cdot 3^{11} \cdot 7^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$168$	$2$	$0$	$1$	$1$		$0$	$1260$	$1.119673$	$38983348653/26353376$	$1.05350$	$6.14520$	$[1, -1, 1, 3967, 38449]$	\(y^2+xy+y=x^3-x^2+3967x+38449\)	168.2.0.?	$[]$