Elliptic curve isogeny class with Cremona label 53130u (LMFDB label 53130.u)

• Label: 53130u
• Number of curves: $4$
• Conductor: $53130$
• CM: no
• Rank: $1$

Elliptic curves in class 53130u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53130.u4	53130u1	\([1, 0, 1, -41654, 3175496]\)	\(7992430388714760409/259528961556480\)	\(259528961556480\)	\([2]\)	\(327680\)	\(1.5396\)	\(\Gamma_0(N)\)-optimal
53130.u2	53130u2	\([1, 0, 1, -661174, 206873672]\)	\(31964658506999396739289/35409164313600\)	\(35409164313600\)	\([2, 2]\)	\(655360\)	\(1.8862\)
53130.u3	53130u3	\([1, 0, 1, -655894, 210341576]\)	\(-31204967494047467761369/1064730266583060000\)	\(-1064730266583060000\)	\([2]\)	\(1310720\)	\(2.2327\)
53130.u1	53130u4	\([1, 0, 1, -10578774, 13242567112]\)	\(130927136818763403860009689/160665120\)	\(160665120\)	\([2]\)	\(1310720\)	\(2.2327\)

Rank

The elliptic curves in class 53130u have rank \(1\).

Complex multiplication

The elliptic curves in class 53130u do not have complex multiplication.

Modular form 53130.2.a.u

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.