# Properties

 Label 15680.ct Number of curves $1$ Conductor $15680$ CM no Rank $0$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

## Elliptic curves in class 15680.ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.ct1 15680dl1 $$[0, 1, 0, 75, 83]$$ $$8192/5$$ $$-28098560$$ $$[]$$ $$3072$$ $$0.11846$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 15680.ct1 has rank $$0$$.

## Complex multiplication

The elliptic curves in class 15680.ct do not have complex multiplication.

## Modular form 15680.2.a.ct

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 2q^{9} - q^{11} + 5q^{13} + q^{15} + q^{17} - 6q^{19} + O(q^{20})$$