Properties

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

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 75712cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.bc1 75712cb1 \([0, -1, 0, -65121, 6420673]\) \(-193100552/91\) \(-14393003835392\) \([]\) \(365568\) \(1.4805\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712cb1 has rank \(0\).

Complex multiplication

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

Modular form 75712.2.a.cb

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{5} - q^{7} - 2 q^{9} + 5 q^{11} - 4 q^{15} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display