Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75712.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.bp1 75712bq1 \([0, 0, 0, -9308, -346736]\) \(-32209663824/117649\) \(-325757845504\) \([]\) \(82944\) \(1.0700\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.bp1 has rank \(0\).

Complex multiplication

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

Modular form 75712.2.a.bp

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 3q^{9} + 2q^{11} - 3q^{17} + 6q^{19} + O(q^{20})\)  Toggle raw display