Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76664.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76664.d1 76664a1 \([0, 0, 0, -44941532, 116236275668]\) \(-15283295882302464/41714923579\) \(-27399444755470617039616\) \([]\) \(5515776\) \(3.1790\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 76664.d1 has rank \(1\).

Complex multiplication

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

Modular form 76664.2.a.d

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