Properties

 Label 303450.cs Number of curves $1$ Conductor $303450$ CM no Rank $0$

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cs1")

sage: E.isogeny_class()

Elliptic curves in class 303450.cs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.cs1 303450cs1 $$[1, 0, 1, -657626, 232443398]$$ $$-288568081/47250$$ $$-5150070923238281250$$ $$[]$$ $$7931520$$ $$2.3179$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 303450.cs1 has rank $$0$$.

Complex multiplication

The elliptic curves in class 303450.cs do not have complex multiplication.

Modular form 303450.2.a.cs

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} - 2q^{11} + q^{12} - 4q^{13} - q^{14} + q^{16} - q^{18} + 6q^{19} + O(q^{20})$$