Elliptic curve isogeny class with Cremona label 76230y (LMFDB label 76230.n)

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

Elliptic curves in class 76230y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
76230.n4	76230y1	\([1, -1, 0, -31785, -23073715]\)	\(-2749884201/176619520\)	\(-228098452780154880\)	\([2]\)	\(983040\)	\(2.0105\)	\(\Gamma_0(N)\)-optimal
76230.n3	76230y2	\([1, -1, 0, -1425705, -650616499]\)	\(248158561089321/1859334400\)	\(2401270821259833600\)	\([2, 2]\)	\(1966080\)	\(2.3571\)
76230.n2	76230y3	\([1, -1, 0, -2384025, 334728125]\)	\(1160306142246441/634128110000\)	\(818956142307508590000\)	\([2]\)	\(3932160\)	\(2.7036\)
76230.n1	76230y4	\([1, -1, 0, -22770105, -41815426339]\)	\(1010962818911303721/57392720\)	\(74120859533785680\)	\([2]\)	\(3932160\)	\(2.7036\)

Rank

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

Complex multiplication

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

Modular form 76230.2.a.y

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.