Elliptic curve isogeny class with LMFDB label 177450.cb (Cremona label 177450iz)

• Label: 177450.cb
• Number of curves: $8$
• Conductor: $177450$
• CM: no
• Rank: $0$

Elliptic curves in class 177450.cb

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
177450.cb1	177450iz8	[1, 1, 0, -1483957400, -22003535520000]	[2]	63700992
177450.cb2	177450iz6	[1, 1, 0, -92749400, -343818168000]	[2, 2]	31850496
177450.cb3	177450iz7	[1, 1, 0, -85989400, -396052688000]	[2]	63700992
177450.cb4	177450iz5	[1, 1, 0, -18410525, -29878254375]	[2]	21233664
177450.cb5	177450iz3	[1, 1, 0, -6221400, -4541880000]	[2]	15925248
177450.cb6	177450iz2	[1, 1, 0, -2440025, 769135125]	[2, 2]	10616832
177450.cb7	177450iz1	[1, 1, 0, -2102025, 1171693125]	[2]	5308416	\(\Gamma_0(N)\)-optimal
177450.cb8	177450iz4	[1, 1, 0, 8122475, 5659572625]	[2]	21233664

Rank

The elliptic curves in class 177450.cb have rank \(0\).

Complex multiplication

The elliptic curves in class 177450.cb do not have complex multiplication.

Modular form 177450.2.a.cb

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.