Properties

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

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Show commands: SageMath
E = EllipticCurve("cl1")
 
E.isogeny_class()
 

Elliptic curves in class 75712.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.cl1 75712bz1 \([0, 1, 0, -49845761, -135707039233]\) \(-10824513276632329/21926008832\) \(-27743395974840867356672\) \([]\) \(9934848\) \(3.1934\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.cl1 has rank \(0\).

Complex multiplication

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

Modular form 75712.2.a.cl

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