Elliptic curve isogeny class with Cremona label 76230dx (LMFDB label 76230.dl)

• Label: 76230dx
• Number of curves: $4$
• Conductor: $76230$
• CM: no
• Rank: $1$

Elliptic curves in class 76230dx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
76230.dl4	76230dx1	\([1, -1, 1, -217823, -33846073]\)	\(885012508801/127733760\)	\(164964059599933440\)	\([2]\)	\(737280\)	\(2.0291\)	\(\Gamma_0(N)\)-optimal
76230.dl2	76230dx2	\([1, -1, 1, -3354143, -2363504569]\)	\(3231355012744321/85377600\)	\(110262435670094400\)	\([2, 2]\)	\(1474560\)	\(2.3756\)
76230.dl3	76230dx3	\([1, -1, 1, -3223463, -2556231433]\)	\(-2868190647517441/527295615000\)	\(-680985396966655935000\)	\([2]\)	\(2949120\)	\(2.7222\)
76230.dl1	76230dx4	\([1, -1, 1, -53665943, -151306557289]\)	\(13235378341603461121/9240\)	\(11933164033560\)	\([2]\)	\(2949120\)	\(2.7222\)

Rank

The elliptic curves in class 76230dx have rank \(1\).

Complex multiplication

The elliptic curves in class 76230dx do not have complex multiplication.

Modular form 76230.2.a.dx

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.