Properties

Label 75712cr
Number of curves $1$
Conductor $75712$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cr1")
 
E.isogeny_class()
 

Elliptic curves in class 75712cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.y1 75712cr1 \([0, -1, 0, 427007, -44690335]\) \(54439939000/36924979\) \(-5840234773283176448\) \([]\) \(967680\) \(2.2896\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712cr1 has rank \(1\).

Complex multiplication

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

Modular form 75712.2.a.cr

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