Elliptic curve isogeny class with LMFDB label 19220.c (Cremona label 19220b)

• Label: 19220.c
• Number of curves: $4$
• Conductor: $19220$
• CM: no
• Rank: $1$

Elliptic curves in class 19220.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19220.c1	19220b3	\([0, -1, 0, -39721, 3059646]\)	\(488095744/125\)	\(1775007362000\)	\([2]\)	\(45360\)	\(1.3363\)
19220.c2	19220b4	\([0, -1, 0, -34916, 3822680]\)	\(-20720464/15625\)	\(-3550014724000000\)	\([2]\)	\(90720\)	\(1.6829\)
19220.c3	19220b1	\([0, -1, 0, -1281, -11710]\)	\(16384/5\)	\(71000294480\)	\([2]\)	\(15120\)	\(0.78704\)	\(\Gamma_0(N)\)-optimal
19220.c4	19220b2	\([0, -1, 0, 3524, -82824]\)	\(21296/25\)	\(-5680023558400\)	\([2]\)	\(30240\)	\(1.1336\)

Rank

The elliptic curves in class 19220.c have rank \(1\).

Complex multiplication

The elliptic curves in class 19220.c do not have complex multiplication.

Modular form 19220.2.a.c

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.