Modular symbols using eclib newforms

class sage.libs.eclib.newforms.ECModularSymbol

Bases: object

Modular symbol associated with an elliptic curve, using John Cremona’s newforms class.

EXAMPLES:

sage: from sage.libs.eclib.newforms import ECModularSymbol
sage: E = EllipticCurve('11a')
sage: M = ECModularSymbol(E,1); M
Modular symbol with sign 1 over Rational Field attached to Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field
sage: [M(1/i) for i in range(1,11)]
[0, 2, 1, -1, -2, -2, -1, 1, 2, 0]

The curve is automatically converted to its minimal model:

sage: E = EllipticCurve([0,0,0,0,1/4])
sage: ECModularSymbol(E)
Modular symbol with sign 1 over Rational Field attached to Elliptic Curve defined by y^2 + y = x^3 over Rational Field