Elliptic curve isogeny class with Cremona label 430950it (LMFDB label 430950.it)

• Label: 430950it
• Number of curves: $4$
• Conductor: $430950$
• CM: no
• Rank: $1$

Elliptic curves in class 430950it

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
430950.it4	430950it1	\([1, 0, 0, 3950287, 2377923417]\)	\(90391899763439/84690294000\)	\(-6387248020185093750000\)	\([2]\)	\(34062336\)	\(2.8712\)	\(\Gamma_0(N)\)-optimal^*
430950.it3	430950it2	\([1, 0, 0, -20470213, 21450333917]\)	\(12577973014374481/4642947562500\)	\(350165954393797851562500\)	\([2, 2]\)	\(68124672\)	\(3.2178\)	\(\Gamma_0(N)\)-optimal^*
430950.it1	430950it3	\([1, 0, 0, -289813963, 1898506927667]\)	\(35694515311673154481/10400566692750\)	\(784399201838530230468750\)	\([2]\)	\(136249344\)	\(3.5644\)	\(\Gamma_0(N)\)-optimal^*
430950.it2	430950it4	\([1, 0, 0, -141854463, -634874305833]\)	\(4185743240664514801/113629394531250\)	\(8569802877937316894531250\)	\([2]\)	\(136249344\)	\(3.5644\)

^*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 430950it1.

Rank

The elliptic curves in class 430950it have rank \(1\).

Complex multiplication

The elliptic curves in class 430950it do not have complex multiplication.

Modular form 430950.2.a.it

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.