Elliptic curve isogeny class with LMFDB label 474075.cr (Cremona label 474075cr)

• Label: 474075.cr
• Number of curves: $4$
• Conductor: $474075$
• CM: no
• Rank: $1$

Elliptic curves in class 474075.cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
474075.cr1	474075cr3	\([1, -1, 0, -7590942, 8051803591]\)	\(36097320816649/80625\)	\(108045211025390625\)	\([2]\)	\(12976128\)	\(2.5136\)	\(\Gamma_0(N)\)-optimal^*
474075.cr2	474075cr4	\([1, -1, 0, -1306692, -413742659]\)	\(184122897769/51282015\)	\(68722804743965859375\)	\([2]\)	\(12976128\)	\(2.5136\)
474075.cr3	474075cr2	\([1, -1, 0, -479817, 122899216]\)	\(9116230969/416025\)	\(557513288891015625\)	\([2, 2]\)	\(6488064\)	\(2.1670\)	\(\Gamma_0(N)\)-optimal^*
474075.cr4	474075cr1	\([1, -1, 0, 16308, 7302091]\)	\(357911/17415\)	\(-23337765581484375\)	\([2]\)	\(3244032\)	\(1.8205\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 474075.cr1.

Rank

The elliptic curves in class 474075.cr have rank \(1\).

Complex multiplication

The elliptic curves in class 474075.cr do not have complex multiplication.

Modular form 474075.2.a.cr

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.