Properties

Label 215475r
Number of curves $1$
Conductor $215475$
CM no
Rank $1$

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

Elliptic curves in class 215475r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215475.j1 215475r1 \([1, 1, 1, -3227988, 11090107296]\) \(-1079309310625/14795494587\) \(-50992114248096578034075\) \([]\) \(32288256\) \(3.0387\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 215475r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 215475r do not have complex multiplication.

Modular form 215475.2.a.r

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