Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 215475i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215475.e1 215475i1 \([0, -1, 1, -18308, 1559768]\) \(-53248/51\) \(-650035418296875\) \([]\) \(1280448\) \(1.5385\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 215475i1 has rank \(1\).

Complex multiplication

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

Modular form 215475.2.a.i

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