# Properties

 Label 10051c Number of curves $1$ Conductor $10051$ CM no Rank $0$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 10051c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10051.b1 10051c1 $$[1, 1, 1, -5830, 158544]$$ $$279841/19$$ $$1487908720339$$ $$[]$$ $$7728$$ $$1.0843$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 10051c1 has rank $$0$$.

## Complex multiplication

The elliptic curves in class 10051c do not have complex multiplication.

## Modular form 10051.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + 3q^{8} - 2q^{9} - q^{10} + 2q^{11} + q^{12} + 4q^{13} - q^{15} - q^{16} - 3q^{17} + 2q^{18} - q^{19} + O(q^{20})$$