Elliptic curve isogeny class with Cremona label 127050fw (LMFDB label 127050.ex)

• Label: 127050fw
• Number of curves: $4$
• Conductor: $127050$
• CM: no
• Rank: $1$

Elliptic curves in class 127050fw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
127050.ex3	127050fw1	\([1, 1, 1, -2997838, 1375739531]\)	\(107639597521009/32699842560\)	\(905152590397440000000\)	\([4]\)	\(7372800\)	\(2.7262\)	\(\Gamma_0(N)\)-optimal
127050.ex2	127050fw2	\([1, 1, 1, -18485838, -29538308469]\)	\(25238585142450289/995844326400\)	\(27565608917523600000000\)	\([2, 2]\)	\(14745600\)	\(3.0728\)
127050.ex4	127050fw3	\([1, 1, 1, 8134162, -107588148469]\)	\(2150235484224911/181905111732960\)	\(-5035250025730536727500000\)	\([2]\)	\(29491200\)	\(3.4194\)
127050.ex1	127050fw4	\([1, 1, 1, -292913838, -1929677780469]\)	\(100407751863770656369/166028940000\)	\(4595787421489687500000\)	\([2]\)	\(29491200\)	\(3.4194\)

Rank

The elliptic curves in class 127050fw have rank \(1\).

Complex multiplication

The elliptic curves in class 127050fw do not have complex multiplication.

Modular form 127050.2.a.fw

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.