Properties

Label 76664.f
Number of curves $1$
Conductor $76664$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 76664.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76664.f1 76664e1 \([0, -1, 0, -16884, 6738725]\) \(-9472/343\) \(-19276487243118448\) \([]\) \(671328\) \(1.8050\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 76664.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 76664.f do not have complex multiplication.

Modular form 76664.2.a.f

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 2 q^{5} - q^{7} + q^{9} - 5 q^{11} - 6 q^{13} - 4 q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display