Elliptic curve isogeny class with Cremona label 19074bc (LMFDB label 19074.ba)

• Label: 19074bc
• Number of curves: $4$
• Conductor: $19074$
• CM: no
• Rank: $1$

Elliptic curves in class 19074bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19074.ba3	19074bc1	\([1, 0, 0, -111849, 14387913]\)	\(6411014266033/296208\)	\(7149741038352\)	\([4]\)	\(110592\)	\(1.5417\)	\(\Gamma_0(N)\)-optimal
19074.ba2	19074bc2	\([1, 0, 0, -117629, 12816909]\)	\(7457162887153/1370924676\)	\(33090788960752644\)	\([2, 2]\)	\(221184\)	\(1.8883\)
19074.ba1	19074bc3	\([1, 0, 0, -559799, -149459481]\)	\(803760366578833/65593817586\)	\(1583275297955488434\)	\([2]\)	\(442368\)	\(2.2349\)
19074.ba4	19074bc4	\([1, 0, 0, 232061, 74572163]\)	\(57258048889007/132611470002\)	\(-3200918507364705138\)	\([2]\)	\(442368\)	\(2.2349\)

Rank

The elliptic curves in class 19074bc have rank \(1\).

Complex multiplication

The elliptic curves in class 19074bc do not have complex multiplication.

Modular form 19074.2.a.bc

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.