Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75712.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.cf1 75712bw1 \([0, 1, 0, 427007, 44690335]\) \(54439939000/36924979\) \(-5840234773283176448\) \([]\) \(967680\) \(2.2896\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.cf1 has rank \(0\).

Complex multiplication

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

Modular form 75712.2.a.cf

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} - 2q^{9} + q^{11} + 4q^{17} - 6q^{19} + O(q^{20})\)  Toggle raw display