# Properties

 Label 12138y Number of curves $1$ Conductor $12138$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 12138y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12138.v1 12138y1 $$[1, 0, 0, 1813, 12849]$$ $$2280364702703/1560674304$$ $$-451034873856$$ $$[]$$ $$24480$$ $$0.92486$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 12138y1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 12138y do not have complex multiplication.

## Modular form 12138.2.a.y

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - 3q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - 3q^{10} - 5q^{11} + q^{12} - q^{14} - 3q^{15} + q^{16} + q^{18} + 6q^{19} + O(q^{20})$$