Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 215475.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215475.z1 215475bg1 \([0, -1, 1, 2817, 51443]\) \(819200/867\) \(-2615527126875\) \([]\) \(224640\) \(1.0694\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 215475.z1 has rank \(1\).

Complex multiplication

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

Modular form 215475.2.a.z

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