Elliptic curve isogeny class with Cremona label 67830i (LMFDB label 67830.f)

• Label: 67830i
• Number of curves: $4$
• Conductor: $67830$
• CM: no
• Rank: $2$

Elliptic curves in class 67830i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
67830.f4	67830i1	\([1, 1, 0, -667, -611]\)	\(32894113444921/18988058880\)	\(18988058880\)	\([2]\)	\(69632\)	\(0.66178\)	\(\Gamma_0(N)\)-optimal
67830.f2	67830i2	\([1, 1, 0, -7147, 228781]\)	\(40382202458800441/165632720400\)	\(165632720400\)	\([2, 2]\)	\(139264\)	\(1.0084\)
67830.f3	67830i3	\([1, 1, 0, -3727, 452449]\)	\(-5727748633923961/85728251227500\)	\(-85728251227500\)	\([2]\)	\(278528\)	\(1.3549\)
67830.f1	67830i4	\([1, 1, 0, -114247, 14815801]\)	\(164916483627583086841/2791475820\)	\(2791475820\)	\([4]\)	\(278528\)	\(1.3549\)

Rank

The elliptic curves in class 67830i have rank \(2\).

Complex multiplication

The elliptic curves in class 67830i do not have complex multiplication.

Modular form 67830.2.a.i

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.