# Properties

 Label 75712.bd Number of curves $1$ Conductor $75712$ CM no Rank $0$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

## Elliptic curves in class 75712.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.bd1 75712be1 $$[0, -1, 0, -49845761, 135707039233]$$ $$-10824513276632329/21926008832$$ $$-27743395974840867356672$$ $$[]$$ $$9934848$$ $$3.1934$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 75712.bd1 has rank $$0$$.

## Complex multiplication

The elliptic curves in class 75712.bd do not have complex multiplication.

## Modular form 75712.2.a.bd

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{5} + q^{7} - 2q^{9} - q^{11} - 4q^{15} + 4q^{17} + 2q^{19} + O(q^{20})$$