Elliptic curve isogeny class with LMFDB label 418950.pt (Cremona label 418950pt)

• Label: 418950.pt
• Number of curves: $4$
• Conductor: $418950$
• CM: no
• Rank: $1$

Elliptic curves in class 418950.pt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
418950.pt1	418950pt3	\([1, -1, 1, -33516230, 74692943147]\)	\(3107086841064961/570\)	\(763854515156250\)	\([2]\)	\(21233664\)	\(2.6915\)	\(\Gamma_0(N)\)-optimal^*
418950.pt2	418950pt4	\([1, -1, 1, -2425730, 774287147]\)	\(1177918188481/488703750\)	\(654909764932089843750\)	\([2]\)	\(21233664\)	\(2.6915\)
418950.pt3	418950pt2	\([1, -1, 1, -2094980, 1167218147]\)	\(758800078561/324900\)	\(435397073639062500\)	\([2, 2]\)	\(10616832\)	\(2.3449\)	\(\Gamma_0(N)\)-optimal^*
418950.pt4	418950pt1	\([1, -1, 1, -110480, 24146147]\)	\(-111284641/123120\)	\(-164992575273750000\)	\([2]\)	\(5308416\)	\(1.9983\)	\(\Gamma_0(N)\)-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 418950.pt1.

Rank

The elliptic curves in class 418950.pt have rank \(1\).

Complex multiplication

The elliptic curves in class 418950.pt do not have complex multiplication.

Modular form 418950.2.a.pt

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.