Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 75712.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.b1 75712s1 \([0, 0, 0, -200044, -34443344]\) \(-19983597574473/3670016\) \(-162590281957376\) \([]\) \(875520\) \(1.7297\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.b1 has rank \(1\).

Complex multiplication

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

Modular form 75712.2.a.b

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - 3 q^{5} - q^{7} + 6 q^{9} + 4 q^{11} + 9 q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display