Elliptic curve isogeny class with Cremona label 91728ei (LMFDB label 91728.el)

• Label: 91728ei
• Number of curves: $4$
• Conductor: $91728$
• CM: no
• Rank: $0$

Elliptic curves in class 91728ei

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
91728.el4	91728ei1	\([0, 0, 0, -137739, -410780230]\)	\(-822656953/207028224\)	\(-72728607580156329984\)	\([2]\)	\(2211840\)	\(2.4903\)	\(\Gamma_0(N)\)-optimal
91728.el3	91728ei2	\([0, 0, 0, -9169419, -10589483590]\)	\(242702053576633/2554695936\)	\(897459653694194712576\)	\([2, 2]\)	\(4423680\)	\(2.8369\)
91728.el2	91728ei3	\([0, 0, 0, -16507659, 8755584698]\)	\(1416134368422073/725251155408\)	\(254779303322060113379328\)	\([2]\)	\(8847360\)	\(3.1835\)
91728.el1	91728ei4	\([0, 0, 0, -146338059, -681371566918]\)	\(986551739719628473/111045168\)	\(39009948938868031488\)	\([2]\)	\(8847360\)	\(3.1835\)

Rank

The elliptic curves in class 91728ei have rank \(0\).

Complex multiplication

The elliptic curves in class 91728ei do not have complex multiplication.

Modular form 91728.2.a.ei

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.