Elliptic curve isogeny class with LMFDB label 19855.b (Cremona label 19855b)

• Label: 19855.b
• Number of curves: $4$
• Conductor: $19855$
• CM: no
• Rank: $1$

Elliptic curves in class 19855.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19855.b1	19855b3	\([1, -1, 1, -21367, -1196484]\)	\(22930509321/6875\)	\(323440431875\)	\([2]\)	\(27648\)	\(1.1866\)
19855.b2	19855b4	\([1, -1, 1, -10537, 409244]\)	\(2749884201/73205\)	\(3443993718605\)	\([2]\)	\(27648\)	\(1.1866\)
19855.b3	19855b2	\([1, -1, 1, -1512, -13126]\)	\(8120601/3025\)	\(142313790025\)	\([2, 2]\)	\(13824\)	\(0.83998\)
19855.b4	19855b1	\([1, -1, 1, 293, -1574]\)	\(59319/55\)	\(-2587523455\)	\([2]\)	\(6912\)	\(0.49341\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 19855.b have rank \(1\).

Complex multiplication

The elliptic curves in class 19855.b do not have complex multiplication.

Modular form 19855.2.a.b

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.