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