Elliptic curve isogeny class with Cremona label 216384ct (LMFDB label 216384.bc)

• Label: 216384ct
• Number of curves: $4$
• Conductor: $216384$
• CM: no
• Rank: $2$

Elliptic curves in class 216384ct

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
216384.bc3	216384ct1	\([0, -1, 0, -14324, 658050]\)	\(43169672512/497007\)	\(3742232098752\)	\([2]\)	\(393216\)	\(1.2254\)	\(\Gamma_0(N)\)-optimal
216384.bc2	216384ct2	\([0, -1, 0, -26329, -592871]\)	\(4188852928/2099601\)	\(1011777364168704\)	\([2, 2]\)	\(786432\)	\(1.5720\)
216384.bc4	216384ct3	\([0, -1, 0, 97151, -4667711]\)	\(26304066424/17629983\)	\(-67965742939078656\)	\([4]\)	\(1572864\)	\(1.9185\)
216384.bc1	216384ct4	\([0, -1, 0, -341889, -76769055]\)	\(1146415874696/1056321\)	\(4072246782492672\)	\([2]\)	\(1572864\)	\(1.9185\)

Rank

The elliptic curves in class 216384ct have rank \(2\).

Complex multiplication

The elliptic curves in class 216384ct do not have complex multiplication.

Modular form 216384.2.a.ct

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.