Properties

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

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