Properties

 Label 257600.dw Number of curves $1$ Conductor $257600$ CM no Rank $1$

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dw1")

sage: E.isogeny_class()

Elliptic curves in class 257600.dw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.dw1 257600dw1 $$[0, 0, 0, 428500, -2176830000]$$ $$84972077055/20040095362$$ $$-2052105765068800000000$$ $$[]$$ $$7741440$$ $$2.7686$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 257600.dw1 has rank $$1$$.

Complex multiplication

The elliptic curves in class 257600.dw do not have complex multiplication.

Modular form 257600.2.a.dw

sage: E.q_eigenform(10)

$$q + q^{7} - 3q^{9} + 4q^{11} + 3q^{13} - q^{17} + O(q^{20})$$