Properties

Label 127050.r
Number of curves $1$
Conductor $127050$
CM no
Rank $2$

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

Elliptic curves in class 127050.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.r1 127050g1 \([1, 1, 0, -28800, 2592000]\) \(-1397395501513/740710656\) \(-1400406084000000\) \([]\) \(829440\) \(1.6104\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 127050.r1 has rank \(2\).

Complex multiplication

The elliptic curves in class 127050.r do not have complex multiplication.

Modular form 127050.2.a.r

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