Elliptic curve isogeny class with Cremona label 6450bd (LMFDB label 6450.t)

• Label: 6450bd
• Number of curves: $4$
• Conductor: $6450$
• CM: no
• Rank: $1$

Elliptic curves in class 6450bd

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
6450.t3	6450bd1	[1, 1, 1, -1713, -27969]	[2]	4608	\(\Gamma_0(N)\)-optimal
6450.t2	6450bd2	[1, 1, 1, -2213, -10969]	[2, 2]	9216
6450.t1	6450bd3	[1, 1, 1, -20963, 1151531]	[2]	18432
6450.t4	6450bd4	[1, 1, 1, 8537, -75469]	[2]	18432

Rank

The elliptic curves in class 6450bd have rank \(1\).

Complex multiplication

The elliptic curves in class 6450bd do not have complex multiplication.

Modular form 6450.2.a.bd

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.