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

• Label: 433200n
• Number of curves: $8$
• Conductor: $433200$
• CM: no
• Rank: $1$

Elliptic curves in class 433200n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
433200.n8	433200n1	\([0, -1, 0, 213592, 116595312]\)	\(357911/2160\)	\(-6503622589440000000\)	\([2]\)	\(7962624\)	\(2.2918\)	\(\Gamma_0(N)\)-optimal^*
433200.n6	433200n2	\([0, -1, 0, -2674408, 1525939312]\)	\(702595369/72900\)	\(219497262393600000000\)	\([2, 2]\)	\(15925248\)	\(2.6384\)	\(\Gamma_0(N)\)-optimal^*
433200.n7	433200n3	\([0, -1, 0, -1952408, -3435644688]\)	\(-273359449/1536000\)	\(-4624798285824000000000\)	\([2]\)	\(23887872\)	\(2.8411\)
433200.n4	433200n4	\([0, -1, 0, -41662408, 103518547312]\)	\(2656166199049/33750\)	\(101619102960000000000\)	\([2]\)	\(31850496\)	\(2.9849\)	\(\Gamma_0(N)\)-optimal^*
433200.n5	433200n5	\([0, -1, 0, -9894408, -10314860688]\)	\(35578826569/5314410\)	\(16001350428493440000000\)	\([2]\)	\(31850496\)	\(2.9849\)
433200.n3	433200n6	\([0, -1, 0, -48160408, -128382076688]\)	\(4102915888729/9000000\)	\(27098427456000000000000\)	\([2, 2]\)	\(47775744\)	\(3.1877\)
433200.n2	433200n7	\([0, -1, 0, -65488408, -27741052688]\)	\(10316097499609/5859375000\)	\(17642205375000000000000000\)	\([2]\)	\(95551488\)	\(3.5343\)
433200.n1	433200n8	\([0, -1, 0, -770160408, -8226334076688]\)	\(16778985534208729/81000\)	\(243885847104000000000\)	\([2]\)	\(95551488\)	\(3.5343\)

^*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 433200n1.

Rank

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

Complex multiplication

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

Modular form 433200.2.a.n

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.