Properties

Label 45486.e
Number of curves $1$
Conductor $45486$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 45486.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
45486.e1 45486r1 \([1, -1, 0, -24435, -36129461]\) \(-361/126\) \(-563162960044053054\) \([]\) \(612864\) \(2.0852\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 45486.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 45486.e do not have complex multiplication.

Modular form 45486.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 2 q^{11} - q^{13} - q^{14} + q^{16} + 2 q^{17} + O(q^{20})\) Copy content Toggle raw display