Elliptic curve isogeny class with LMFDB label 43350.e (Cremona label 43350n)

• Label: 43350.e
• Number of curves: $4$
• Conductor: $43350$
• CM: no
• Rank: $1$

Elliptic curves in class 43350.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
43350.e1	43350n4	\([1, 1, 0, -47258875, -125064996875]\)	\(30949975477232209/478125000\)	\(180324612158203125000\)	\([2]\)	\(5308416\)	\(3.0219\)
43350.e2	43350n2	\([1, 1, 0, -3041875, -1832217875]\)	\(8253429989329/936360000\)	\(353147720450625000000\)	\([2, 2]\)	\(2654208\)	\(2.6753\)
43350.e3	43350n1	\([1, 1, 0, -729875, 209278125]\)	\(114013572049/15667200\)	\(5908876891200000000\)	\([2]\)	\(1327104\)	\(2.3287\)	\(\Gamma_0(N)\)-optimal
43350.e4	43350n3	\([1, 1, 0, 4183125, -9208942875]\)	\(21464092074671/109596256200\)	\(-41334174940143403125000\)	\([2]\)	\(5308416\)	\(3.0219\)

Rank

The elliptic curves in class 43350.e have rank \(1\).

Complex multiplication

The elliptic curves in class 43350.e do not have complex multiplication.

Modular form 43350.2.a.e

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.