Elliptic curve isogeny class with LMFDB label 433200.ic (Cremona label 433200ic)

• Label: 433200.ic
• Number of curves: $4$
• Conductor: $433200$
• CM: no
• Rank: $1$

Elliptic curves in class 433200.ic

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
433200.ic1	433200ic3	\([0, 1, 0, -22024008, 39773651988]\)	\(784767874322/35625\)	\(53632304340000000000\)	\([2]\)	\(26542080\)	\(2.8619\)	\(\Gamma_0(N)\)-optimal^*
433200.ic2	433200ic4	\([0, 1, 0, -6862008, -6409800012]\)	\(23735908082/1954815\)	\(2942911803744480000000\)	\([2]\)	\(26542080\)	\(2.8619\)
433200.ic3	433200ic2	\([0, 1, 0, -1447008, 553889988]\)	\(445138564/81225\)	\(61140826947600000000\)	\([2, 2]\)	\(13271040\)	\(2.5153\)	\(\Gamma_0(N)\)-optimal^*
433200.ic4	433200ic1	\([0, 1, 0, 177492, 50294988]\)	\(3286064/7695\)	\(-1448072217180000000\)	\([2]\)	\(6635520\)	\(2.1687\)	\(\Gamma_0(N)\)-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 433200.ic1.

Rank

The elliptic curves in class 433200.ic have rank \(1\).

Complex multiplication

The elliptic curves in class 433200.ic do not have complex multiplication.

Modular form 433200.2.a.ic

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.