Elliptic curve isogeny class with Cremona label 248256u (LMFDB label 248256.u)

• Label: 248256u
• Number of curves: $4$
• Conductor: $248256$
• CM: no
• Rank: $1$

Elliptic curves in class 248256u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
248256.u4	248256u1	\([0, 0, 0, 222324, -120688400]\)	\(6359387729183/36606836736\)	\(-6995675442195726336\)	\([2]\)	\(4055040\)	\(2.2980\)	\(\Gamma_0(N)\)-optimal
248256.u3	248256u2	\([0, 0, 0, -2726796, -1565757200]\)	\(11733138754458337/1248028591104\)	\(238501977893061525504\)	\([2, 2]\)	\(8110080\)	\(2.6445\)
248256.u2	248256u3	\([0, 0, 0, -10191756, 10829062384]\)	\(612637130696707297/89442530521632\)	\(17092733763654707576832\)	\([2]\)	\(16220160\)	\(2.9911\)
248256.u1	248256u4	\([0, 0, 0, -42447756, -106444979984]\)	\(44260923429070723297/593700376032\)	\(113457908712034271232\)	\([2]\)	\(16220160\)	\(2.9911\)

Rank

The elliptic curves in class 248256u have rank \(1\).

Complex multiplication

The elliptic curves in class 248256u do not have complex multiplication.

Modular form 248256.2.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.