Properties

Label 63175.r
Number of curves $1$
Conductor $63175$
CM no
Rank $1$

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

Elliptic curves in class 63175.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63175.r1 63175t1 \([1, -1, 0, -10717, -99134]\) \(12825/7\) \(74303088304375\) \([]\) \(414504\) \(1.3524\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 63175.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 63175.r do not have complex multiplication.

Modular form 63175.2.a.r

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