Elliptic curve isogeny class with Cremona label 58800u (LMFDB label 58800.bw)

• Label: 58800u
• Number of curves: $4$
• Conductor: $58800$
• CM: no
• Rank: $2$

Elliptic curves in class 58800u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
58800.bw4	58800u1	\([0, -1, 0, 4492, -55488]\)	\(21296/15\)	\(-7058940000000\)	\([2]\)	\(110592\)	\(1.1539\)	\(\Gamma_0(N)\)-optimal
58800.bw3	58800u2	\([0, -1, 0, -20008, -447488]\)	\(470596/225\)	\(423536400000000\)	\([2, 2]\)	\(221184\)	\(1.5005\)
58800.bw2	58800u3	\([0, -1, 0, -167008, 26012512]\)	\(136835858/1875\)	\(7058940000000000\)	\([2]\)	\(442368\)	\(1.8471\)
58800.bw1	58800u4	\([0, -1, 0, -265008, -52387488]\)	\(546718898/405\)	\(1524731040000000\)	\([2]\)	\(442368\)	\(1.8471\)

Rank

The elliptic curves in class 58800u have rank \(2\).

Complex multiplication

The elliptic curves in class 58800u do not have complex multiplication.

Modular form 58800.2.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.