Properties

Label 215475.a
Number of curves $1$
Conductor $215475$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 215475.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215475.a1 215475g1 \([0, -1, 1, -26758, 1703418]\) \(-4747964416/31875\) \(-14224716796875\) \([]\) \(1032192\) \(1.3590\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 215475.a1 has rank \(2\).

Complex multiplication

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

Modular form 215475.2.a.a

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