# Properties

 Label 257600dg Number of curves $1$ Conductor $257600$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dg1")

sage: E.isogeny_class()

## Elliptic curves in class 257600dg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.dg1 257600dg1 $$[0, 0, 0, 17140, 17414640]$$ $$84972077055/20040095362$$ $$-131334768964403200$$ $$[]$$ $$1548288$$ $$1.9639$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 257600dg1 has rank $$1$$.

## Complex multiplication

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

## Modular form 257600.2.a.dg

sage: E.q_eigenform(10)

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