Properties

 Label 270802d Number of curves $1$ Conductor $270802$ CM no Rank $2$

Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

Elliptic curves in class 270802d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.d1 270802d1 $$[1, 1, 0, 215, -1777]$$ $$1297427375/2540258$$ $$-2136356978$$ $$[]$$ $$101760$$ $$0.47472$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 270802d1 has rank $$2$$.

Complex multiplication

The elliptic curves in class 270802d do not have complex multiplication.

Modular form 270802.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} - 2q^{9} - 3q^{11} - q^{12} - 2q^{13} - q^{14} + q^{16} - 2q^{17} + 2q^{18} + 3q^{19} + O(q^{20})$$