Properties

Label 66300r
Number of curves $1$
Conductor $66300$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 66300r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66300.e1 66300r1 \([0, -1, 0, -918958, -1174055063]\) \(-8582447853100000000/54611490800928087\) \(-546114908009280870000\) \([]\) \(2661120\) \(2.6626\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66300r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 66300r do not have complex multiplication.

Modular form 66300.2.a.r

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