Elliptic curve isogeny class with LMFDB label 127050.gr (Cremona label 127050gb)

• Label: 127050.gr
• Number of curves: $8$
• Conductor: $127050$
• CM: no
• Rank: $0$

Elliptic curves in class 127050.gr

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
127050.gr1	127050gb8	[1, 1, 1, -19514338, -20882966719]	[2]	19906560
127050.gr2	127050gb5	[1, 1, 1, -17427088, -28009019719]	[2]	6635520
127050.gr3	127050gb6	[1, 1, 1, -8170588, 8746908281]	[2, 2]	9953280
127050.gr4	127050gb3	[1, 1, 1, -8110088, 8886300281]	[2]	4976640
127050.gr5	127050gb2	[1, 1, 1, -1092088, -435539719]	[2, 2]	3317760
127050.gr6	127050gb4	[1, 1, 1, -245088, -1092811719]	[2]	6635520
127050.gr7	127050gb1	[1, 1, 1, -124088, 5868281]	[2]	1658880	\(\Gamma_0(N)\)-optimal
127050.gr8	127050gb7	[1, 1, 1, 2205162, 29456905281]	[2]	19906560

Rank

The elliptic curves in class 127050.gr have rank \(0\).

Modular form 127050.2.a.gr

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.