Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: 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)
 
\(q + 2q^{3} - 2q^{5} - q^{7} + q^{9} - 5q^{11} - 6q^{13} - 4q^{15} + 2q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display