Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75712.cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.cs1 75712cc1 \([0, -1, 0, -38081, 3786977]\) \(-114244/49\) \(-2619526698041344\) \([]\) \(399360\) \(1.6660\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.cs1 has rank \(0\).

Complex multiplication

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

Modular form 75712.2.a.cs

sage: E.q_eigenform(10)
 
\(q + 2q^{3} - q^{5} - q^{7} + q^{9} + 2q^{11} - 2q^{15} - 3q^{17} - 8q^{19} + O(q^{20})\)  Toggle raw display