Elliptic curve isogeny class with LMFDB label 414050.hq (Cremona label 414050hq)

• Label: 414050.hq
• Number of curves: $2$
• Conductor: $414050$
• CM: no
• Rank: $1$

Elliptic curves in class 414050.hq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
414050.hq1	414050hq2	\([1, 1, 1, -5032063, 4342539781]\)	\(544737993463/20000\)	\(517373589687500000\)	\([2]\)	\(17694720\)	\(2.4866\)	\(\Gamma_0(N)\)-optimal^*
414050.hq2	414050hq1	\([1, 1, 1, -300063, 74275781]\)	\(-115501303/25600\)	\(-662238194800000000\)	\([2]\)	\(8847360\)	\(2.1400\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 414050.hq1.

Rank

The elliptic curves in class 414050.hq have rank \(1\).

Complex multiplication

The elliptic curves in class 414050.hq do not have complex multiplication.

Modular form 414050.2.a.hq

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.