Properties

Label 6630.r
Number of curves $1$
Conductor $6630$
CM no
Rank $1$

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

Elliptic curves in class 6630.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6630.r1 6630u1 \([1, 1, 1, -1410, 19815]\) \(-310027558782241/414375000\) \(-414375000\) \([]\) \(8064\) \(0.55946\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6630.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6630.r do not have complex multiplication.

Modular form 6630.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{10} + 5 q^{11} - q^{12} + q^{13} - 4 q^{14} - q^{15} + q^{16} + q^{17} + q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display