Properties

 Label 422331ca Number of curves $1$ Conductor $422331$ CM no Rank $1$

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ca1")

sage: E.isogeny_class()

Elliptic curves in class 422331ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422331.ca1 422331ca1 $$[0, 1, 1, -2760, 98375]$$ $$-692224/867$$ $$-2913270068163$$ $$[]$$ $$1726560$$ $$1.0851$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 422331ca1 has rank $$1$$.

Complex multiplication

The elliptic curves in class 422331ca do not have complex multiplication.

Modular form 422331.2.a.ca

sage: E.q_eigenform(10)

$$q + 2q^{2} + q^{3} + 2q^{4} - 4q^{5} + 2q^{6} + q^{9} - 8q^{10} + 4q^{11} + 2q^{12} - 4q^{15} - 4q^{16} - q^{17} + 2q^{18} + 4q^{19} + O(q^{20})$$