# Properties

 Label 25857p Number of curves $1$ Conductor $25857$ CM no Rank $2$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 25857p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25857.a1 25857p1 $$[0, 0, 1, -507, 7816]$$ $$-692224/867$$ $$-18051780123$$ $$[]$$ $$41856$$ $$0.66141$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 25857p1 has rank $$2$$.

## Complex multiplication

The elliptic curves in class 25857p do not have complex multiplication.

## Modular form 25857.2.a.p

sage: E.q_eigenform(10)

$$q - 2q^{2} + 2q^{4} - 4q^{5} - 3q^{7} + 8q^{10} - 4q^{11} + 6q^{14} - 4q^{16} - q^{17} - 4q^{19} + O(q^{20})$$