Elliptic curve isogeny class with Cremona label 19350ba (LMFDB label 19350.e)

• Label: 19350ba
• Number of curves: $4$
• Conductor: $19350$
• CM: no
• Rank: $1$

Elliptic curves in class 19350ba

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
19350.e3	19350ba1	[1, -1, 0, -15417, 739741]	[2]	36864	\(\Gamma_0(N)\)-optimal
19350.e2	19350ba2	[1, -1, 0, -19917, 276241]	[2, 2]	73728
19350.e1	19350ba3	[1, -1, 0, -188667, -31280009]	[2]	147456
19350.e4	19350ba4	[1, -1, 0, 76833, 2114491]	[2]	147456

Rank

The elliptic curves in class 19350ba have rank \(1\).

Complex multiplication

The elliptic curves in class 19350ba do not have complex multiplication.

Modular form 19350.2.a.ba

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.